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Data Preparation for Machine Learning Projects

The data we collect for machine-learning must be pre-processed before it can be used to fit a model. Data preparation is essentially, the task of modifying raw data into a form that can be used for modelling, mostly by data addition, deletion or other data transformation techniques.  We need to pre-process the data before feeding into any algorithm mainly due to the following reasons: Messy data – Real world data is messy, with missing values, redundant values, out-of-range values, errors and noise. Machine learning algorithms need numeric data. More often than not, algorithms have requirements on the input data, for example some algorithms assume a certain probability distribution of the data, others might perform worse if the predictor variables are highly correlated etc. Data preparation tasks are mostly dependent on the dataset we are working with, and to some extent on the choice of model. However, it becomes more evident after initial analysis of the data and EDA. For e.g. looking at the summary statistics, we know if predictors need to be scaled. Looking at correlation matrix you can find out if there are highly correlated predictors. Looking at various plots, e.g. boxplot, you can find, if outliers need to be dealt with, so on and so forth. Even though every dataset is different, we can define a few common steps which can guide us in preparing the data to feed into our learning algorithms. Some common tasks that contribute to data pre-processing are: Data Cleaning Feature Selection Data Transformation Feature Engineering Dimensionality Reduction Note: Throughout this article, we will refer to Python libraries and syntaxes. Data Cleaning: It can be summed up as the process of correcting the errors in the data. Errors could be in the form of missing values, redundant rows or columns, variables with zero or near zero variance and so on. Thus, data cleaning involves a few or all of the below sub-tasks: Redundant samples or duplicate rows: should be identified and dropped from the dataset. In Python,  functions in Pandas such as duplicated() can be used to identify such samples and drop_duplicates() can be used to drop such rows. Redundant Features: If the dataset has features which are highly correlated, it may lead to multi-collinearity (irregular regression coefficient estimates). Such columns can be identified using the correlation matrix and one of the pairs of the highly correlated feature should be dropped. Similarly, near zero variance features, which have the same value for all the samples do not contribute to the variance in data. Such columns should be identified and dropped from the dataset.  Outlier Detection: Outliers are extreme values which fall far away from other observations. Outliers can skew the descriptive statistics of the data, hence mislead data interpretations and negatively impact model performance. So, it is important that the outliers are detected and dealt with. Outliers can be detected through data visualization techniques like box-plots and scatter plots.  Example of outliers being detected using box plots:  Image Source Outliers can also be detected by computing the z-scores or the Inter-Quartile range. When using z-score, a data point which is more than 3 standard deviations away from the mean is normally considered as an outlier.  However, this may vary based on the size of the dataset. When using inter-quartile range, a point which is below Q1 - 1.5 inter-quartile range or above Q3 + 1.5 inter-quartile range is considered to be an outlier, where Q1 is the first quartile and Q3 is the third quartile. Below diagram shows outliers which are more than 3 standard deviations from the mean: Image Source If there are a few outliers, you may choose to drop the samples with outliers. Else if there are too many outliers, these can be modelled separately. We may also choose to cap or floor the outlier values by the 95th percentile or 5th percentile value. However, you may choose the appropriate replacement value by analyzing the deciles of the data. Missing Values: Data with missing values cannot be used for modelling; hence any missing values should be identified and cleaned. If the data in the predictor or sample is sparse, we may choose to drop the entire column/row. Else we may impute the missing value with mean or median. Missing values in categorical variables can be replaced with the most frequent class. Points to remember: Use z-score for outlier detection if the data follows Gaussian distribution, else use Inter-Quartile range for outlier detection. Feature Selection: Sometimes datasets have hundreds of input variables, not all of which are good predictors of the target and may contribute to noise in the data. Feature selection techniques are used to find the input variables that can most efficiently predict the target variable, in order to reduce the number of input variables. Feature selection techniques can be further classified as supervised selection techniques and unsupervised selection techniques. As the name suggests, unsupervised selection techniques do not consider the target variable while eliminating the input variables. This would include techniques like using correlation to eliminate highly correlated predictors or eliminating low variance predictors. Supervised feature selection techniques consider the target variable for selecting the features to be eliminated. These can be further divided into three groups namely, Intrinsic, Filter and Wrapper techniques. Intrinsic – the feature selection process is embedded in the model building process itself, for e.g. tree-based algorithms which pick up the best predictor for the split. Similarly, regularization techniques like lasso shrinks the coefficient of the predictors such that the coefficient can be shrunk to zero for some predictors, and hence are excluded from the model. Multivariate adaptive regression spline (MARS) models also fall under this category. A major advantage of such methods is that since the feature selection is a part of model building process, it is relatively fast. However model dependance can also prove to be disadvantageous for e.g. some tree-based algorithms are greedy and hence may select predictors which may lead to sub-optimal fit. Filter – Filter based selection techniques use some statistical method to score each predictor separately with the target variable and choose the predictors with highest scores. It is mostly univariate analysis, i.e., each predictor is evaluated in isolation. It does not consider the correlation of independent variables amongst themselves. Based on the type of the input variable i.e., numerical or categorical and the type of output variable an appropriate statistical measure can be used to evaluate predictors for feature selection: for example, Pearson’s correlation coefficient, Spearmon’s correlation coefficient, ANOVA, Chi-square. Wrapper – Wrapper feature selection builds models using various subsets of predictors iteratively, and evaluates the model, until it finds a subset of features which best predict the target. These methods are agnostic to the type of variables. However, they are computationally more taxing. RFE is a commonly used wrapper-based feature selection method. Recursive Feature Elimination is a greedy backward elimination technique, which starts with a complete set of predictors and systematically eliminates less useful predictors, until it finds a subset of predictors which best predict the target variable with the specified number of predictors. Two important hyperparameters for RFE algorithm in scikit learn are the number of predictors(n_features_to_select) and the algorithm of choice (estimator). Points to remember: Feature selection techniques reduce the number of features by excluding or eliminating the existing features from the dataset, whereas dimensionality reduction techniques create a projection of the data in lower dimensional feature space, which does not have a one-to-one mapping with the existing features. However, both have a similar goal of reducing the number of independent variables. Data Transformations: We may need to transform data to change its data type, scale or distribution. Type: We need to analyze the input variables at the very beginning to understand if the predictors are represented with the appropriate data type, and do the required conversions before progressing with the EDA and modelling. For e.g., sometimes the Boolean values are encoded as true and false, and we may transform them to take values 0 and 1. Similarly sometimes we may come across integer variables where it might be more appropriate to treat it as a categorical variable. For e.g. when working on a dataset to predict car prices, it would be more appropriate to treat the variable ‘Number of doors’ which takes up values {2,4} as a categorical variable.  Categorical variables should be converted to numeric, before they can be used for modelling. There are many categorical variable encoding techniques like, N-1 dummy encoding, 1 Hot encoding, label encoding, frequency encoding. Ordinal encoding can be used when we want to specify and maintain the order of the ordinal variable. Scale: Predictor variables may have different units (Km, $, years etc.) and hence, different scales. For e.g. we might have input variables like age and salary in a dataset. Scale of the variable salary will always be much higher than the age, and hence may contribute unequally to the model and create a bias. Hence, we transform the predictors to bring them to a common scale. Normalization and standardization are the most widely used scaling techniques. Normalization: helps scale the data such that all values lie between the range of 0 and 1. The scikit-learn library method even allows one to specify the preferred range. Data shown before and after normalization:  Image SourceStandarisation: We standardize the data by centering it around the mean and then scaling the data by the standard deviation. In other words, mean of the variable is subtracted from each value of the input variable and the difference is divided by the standard deviation of the variable. The resulting data will have zero mean and standard deviation 1. Standardisation assumes that the data follows a Gaussian distribution. Scikit learn library in python can be used for normalization (MinMaxScaler()) and standardization (StandardScaler()).  Data shown before and after standardization:  Image Source Distribution: Many algorithms assume Gaussian distribution for the underlying data. If the data is not Gaussian or is Gaussian like, we can transform the data to reduce the skewness. Box-Cox transform, or Yeo-Johnson transform can be used to perform power transformations on the data. Box-Cox transform applies a different transformation on the data based on the value of lambda. For e.g. for Lambda = -1, it does inverse transformation, for Lambda=0 it does log transformation, for Lambda = 0.5, it does square root transformation, for Lambda = -0.5 it does reciprocal square root transformation. PowerTransformer() class in the python scikit library can be used for making these power transformations.Data shown before and after log transformation: Image SourcePoints to remember: Data transformations should be done on the training dataset, so that the statistic required for transformation is estimated from the training set only and then applied on the validation set. Decision trees and other tree-based ensembles like Random forest and boosting algorithms are not impacted by different scale of the input variables. Hence scaling may not be required.  Linear regression and neural networks which use weighted sum of the input variables and K-nearest neighbors or SVM which compute distance or dot product between predictors will be impacted by the scale of the predictors, hence input variables should be scaled for these models. Between normalization and standardization, one should standardize when the data follows a Gaussian distribution, else normalize. Feature Engineering:  is the part of data pre-processing where we derive new features using one or more existing features. For e.g. when working on taxi fare prediction problem, we may derive a new feature, distance travelled in the ride with the use of latitude and longitude co-ordinates of the start and end point of the ride. Or when working on predicting sales or foot fall for a retail business we may need to add a new feature to factor in, the impact of holiday, weekends and festivals on the target variable. Hence, we may need to engineer these new predictors and feed them into our model to identify the underlying patterns effectively. Polynomial term: We may also add new features by raising the existing input variables to a higher degree polynomial. Polynomial terms help the model learn the non-linear patterns. When polynomial terms of existing features are added to the linear regression model, it is termed as polynomial regression. Usually, we stick to a smaller degree of 2 or 3. Interaction term: We may add new features that represent interaction between existing features by adding a product of two features. For e.g. if we are working on a problem to help businesses allocate their marketing budget between various marketing mediums like radio, TV and newspaper, we need to model how effective each medium is. We may like to factor in the interaction term of a radio and newspaper campaign, to understand the effectiveness of marketing if both the radio and newspaper campaigns were run together at the same time. Similarly, when predicting a crop yield, we may engineer a new interaction term for fertilizer and water together to factor in how the yield varies when water and fertilizer are provided together. Points to remember: When using polynomial terms in the model, it is good practice to restrict the degree of the polynomial to 3 or at most 4. This is firstly, to control the number of input variables. Secondly, a larger degree of the polynomial will result in large values which may impact the weights(parameters) to be large and hence make the model less sensitive to small changes. Domain knowledge or the advice of the SME may come in handy to identify effective interaction terms. Dimensionality Reduction: Sometimes data might have hundreds and even thousands of features. High dimensional data can be more complicated, with way more parameters to train and a very complicated model structure. In higher dimensions, the volume of space is huge, and the data points become sparse, which could negatively impact the machine learning algorithm performance. This is sometimes also referred to as the curse of dimensionality.  Dimensionality Reduction techniques are used to reduce the number of predictor variables in the dataset. Some techniques for dimensionality reduction are: PCA or Principal Component Analysis uses linear algebra and Eigenvalue to achieve dimensionality reduction. For given datapoints PCA finds orthogonal set of directions, that have maximum variance. Rotating the reference frame, it finds the directions (ones which correspond to smallest eigen values) which can be neglected. Principal Component Analysis applied to a dataset is shown below: Manifold learning is a non-linear dimensionality reduction technique which uses geometric properties of the data, to create low dimensional projections of a high dimensional data, while preserving its structure and relationships, and to visualize high dimensional data, which is otherwise difficult. SOM Self organizing Map also called Kohonen map and t-SNE are examples of Manifold learning techniques.  t-distributed stochastic neighbor embedding (t-SNE) computes the probability that pairs of datapoints (in high dimension) are related and maps them in low dimension, such that data has a similar distribution. Autoencoders are deep learning neural networks that learn low dimensional representation of a given dataset in an unsupervised manner. The hidden layer is limited to contain fewer neurons, thus it learns to map high dimensional input vector into low dimensional vector, while still preserving the underlying structure and relationships in the data. Autoencoders have two parts, encoder which learns to map high dimensional vector to a low-dimensional space and decoder, which maps the data from low to high dimension. The output from the encoder with reduced dimension can be fed into any another model for supervised learning. Points to remember:  Dimensionality reduction is mostly performed after data cleaning and data scaling.  It is imperative that the dimensionality reduction performed on the training data set must also be performed on the validation and the new data on which the model will predict. Conclusion:Data preparation is an important and integral step of machine learning projects. There are multiple techniques for various data cleaning tasks. However, there are no best or worst data cleaning techniques. Every machine learning problem is unique and so is the underlying data. We need to apply different techniques and see what works best based on the data and the problem at hand.  

Data Preparation for Machine Learning Projects

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Data Preparation for Machine Learning Projects

The data we collect for machine-learning must be pre-processed before it can be used to fit a model. Data preparation is essentially, the task of modifying raw data into a form that can be used for modelling, mostly by data addition, deletion or other data transformation techniques 

We need to pre-process the data before feeding into any algorithm mainly due to the following reasons: 

  1. Messy data – Real world data is messy, with missing values, redundant values, out-of-range values, errors and noise. 
  2. Machine learning algorithms need numeric data. 
  3. More often than not, algorithms have requirements on the input data, for example some algorithms assume a certain probability distribution of the data, others might perform worse if the predictor variables are highly correlated etc. 

Data preparation tasks are mostly dependent on the dataset we are working with, and to some extent on the choice of model. However, it becomes more evident after initial analysis of the data and EDA. For e.g. looking at the summary statistics, we know if predictors need to be scaled. Looking at correlation matrix you can find out if there are highly correlated predictors. Looking at various plots, e.g. boxplot, you can find, if outliers need to be dealt with, so on and so forth. 

Even though every dataset is different, we can define a few common steps which can guide us in preparing the data to feed into our learning algorithms. 

Some common tasks that contribute to data pre-processing are: 

  1. Data Cleaning 
  2. Feature Selection 
  3. Data Transformation 
  4. Feature Engineering 
  5. Dimensionality Reduction 

Note: Throughout this article, we will refer to Python libraries and syntaxes. 

  • Data Cleaning: It can be summed up as the process of correcting the errors in the data. Errors could be in the form of missing values, redundant rows or columns, variables with zero or near zero variance and so onThus, data cleaning involves a few or all of the below sub-tasks: 
  • Redundant samples or duplicate rowsshould be identified and dropped from the dataset. In Python,  functions in Pandas such as duplicated() can be used to identify such samples and drop_duplicates() can be used to drop such rows. 
  • Redundant Features: If the dataset has features which are highly correlated, it may lead to multi-collinearity (irregular regression coefficient estimates)Such columns can be identified using the correlation matrix and one of the pairs of the highly correlated feature should be dropped. Similarly, near zero variance featureswhich have the same value for all the samples do not contribute to the variance in data. Such columns should be identified and dropped from the dataset.  

  • Outlier Detection: Outliers are extreme values which fall far away from other observations. Outliers can skew the descriptive statistics of the data, hence mislead data interpretations and negatively impact model performance. So, it is important that the outliers are detected and dealt with. Outliers can be detected through data visualization techniques like box-plots and scatter plots.  

Example of outliers being detected using box plots:  

Data Preparation for Machine Learning Projects

Image Source 

Outliers can also be detected by computing the z-scores or the Inter-Quartile range. When using z-score, a data point which is more than 3 standard deviations away from the mean is normally considered as an outlier.  However, this may vary based on the size of the dataset. When using inter-quartile range, a point which is below Q1 - 1.5 inter-quartile range or above Q3 + 1.5 inter-quartile range is considered to be an outlier, where Q1 is the first quartile and Q3 is the third quartile. 

Below diagram shows outliers which are more than 3 standard deviations from the mean: 

Data Preparation for Machine Learning ProjectsImage Source 

If there are few outliers, you may choose to drop the samples with outliers. Else if there are too many outliers, these can be modelled separately. We may also choose to cap or floor the outlier values by the 95th percentile or 5th percentile value. However, you may choose the appropriate replacement value by analyzing the deciles of the data. 

  • Missing Values: Data with missing values cannot be used for modelling; hence any missing values should be identified and cleaned. If the data in the predictor or sample is sparse, we may choose to drop the entire column/row. Else we may impute the missing value with mean or median. Missing values in categorical variables can be replaced with the most frequent class. 

Points to remember: 

  • Use z-score for outlier detection if the data follows Gaussian distribution, else use Inter-Quartile range for outlier detection. 

Feature Selection: Sometimes datasets have hundreds of input variables, not all of which are good predictors of the target and may contribute to noise in the data. Feature selection techniques are used to find the input variables that can most efficiently predict the target variable, in order to reduce the number of input variables. Feature selection techniques can be further classified as supervised selection techniques and unsupervised selection techniques. As the name suggests, unsupervised selection techniques do not consider the target variable while eliminating the input variables. This would include techniques like using correlation to eliminate highly correlated predictors or eliminating low variance predictors. Supervised feature selection techniques consider the target variable for selecting the features to be eliminated. These can be further divided into three groups namely, Intrinsic, Filter and Wrapper techniques. 

  • Intrinsic  the feature selection process is embedded in the model building process itself, for e.g. tree-based algorithms which pick up the best predictor for the split. Similarly, regularization techniques like lasso shrinks the coefficient of the predictors such that the coefficient can be shrunk to zero for some predictors, and hence are excluded from the model. Multivariate adaptive regression spline (MARS) models also fall under this category. A major advantage of such methods is that since the feature selection is a part of model building process, it is relatively fast. However model dependance can also prove to be disadvantageous for e.g. some tree-based algorithms are greedy and hence may select predictors which may lead to sub-optimal fit. 

  • Filter  Filter based selection techniques use some statistical method to score each predictor separately with the target variable and choose the predictors with highest scores. It is mostly univariate analysis, i.e., each predictor is evaluated in isolation. It does not consider the correlation of independent variables amongst themselves. 

Based on the type of the input variable i.e., numerical or categorical and the type of output variable an appropriate statistical measure can be used to evaluate predictors for feature selection: for examplePearson’s correlation coefficient, Spearmon’s correlation coefficient, ANOVA, Chi-square. 

  • Wrapper  Wrapper feature selection builds models using various subsets of predictors iteratively, and evaluates the model, until it finds a subset of features which best predict the target. These methods are agnostic to the type of variables. However, they are computationally more taxing. RFE is a commonly used wrapper-based feature selection method. 

Recursive Feature Elimination is a greedy backward elimination technique, which starts with a complete set of predictors and systematically eliminates less useful predictors, until it finds a subset of predictors which best predict the target variable with the specified number of predictors. Two important hyperparameters for RFE algorithm in scikit learn are the number of predictors(n_features_to_select) and the algorithm of choice (estimator). 

Points to remember: 

  • Feature selection techniques reduce the number of features by excluding or eliminating the existing features from the dataset, whereas dimensionality reduction techniques create a projection of the data in lower dimensional feature space, which does not have a one-to-one mapping with the existing features. However, both have a similar goal of reducing the number of independent variables. 

Data Transformations: We may need to transform data to change its data type, scale or distribution. 

Type: We need to analyze the input variables at the very beginning to understand if the predictors are represented with the appropriate data type, and do the required conversions before progressing with the EDA and modelling. For e.g., sometimes the Boolean values are encoded as true and false, and we may transform them to take values 0 and 1. Similarly sometimes we may come across integer variables where it might be more appropriate to treat it as a categorical variable. For e.g. when working on a dataset to predict car prices, it would be more appropriate to treat the variable ‘Number of doors’ which takes up values {2,4} as a categorical variable.  

Categorical variables should be converted to numeric, before they can be used for modelling. There are many categorical variable encoding techniques like, N-1 dummy encoding, 1 Hot encoding, label encoding, frequency encoding. Ordinal encoding can be used when we want to specify and maintain the order of the ordinal variable. 

Scale: Predictor variables may have different units (Km, $, years etc.) and hence, different scales. For e.g. we might have input variables like age and salary in a dataset. Scale of the variable salary will always be much higher than the age, and hence may contribute unequally to the model and create a bias. Hence, we transform the predictors to bring them to a common scale. Normalization and standardization are the most widely used scaling techniques. 

  • Normalization: helps scale the data such that all values lie between the range of 0 and 1. The scikit-learn library method even allows one to specify the preferred range. 

Data Preparation for Machine Learning Projects

Data shown before and after normalization:  Data Preparation for Machine Learning Projects

Image Source

  • Standarisation: We standardize the data by centering it around the mean and then scaling the data by the standard deviation. In other words, mean of the variable is subtracted from each value of the input variable and the difference is divided by the standard deviation of the variable. The resulting data will have zero mean and standard deviation 1. Standardisation assumes that the data follows a Gaussian distribution. Scikit learn library in python can be used for normalization (MinMaxScaler()) and standardization (StandardScaler()).  

Data Preparation for Machine Learning Projects

Data shown before and after standardization:  

Data Preparation for Machine Learning Projects

Image Source 

  • Distribution: Many algorithms assume Gaussian distribution for the underlying data. If the data is not Gaussian or is Gaussian like, we can transform the data to reduce the skewness. Box-Cox transform, or Yeo-Johnson transform can be used to perform power transformations on the data. Box-Cox transform applies a different transformation othe data based on the value of lambda. For e.g. for Lambda = -1, it does inverse transformation, for Lambda=0 it does log transformation, for Lambda = 0.5, it does square root transformation, for Lambda = -0.5 it does reciprocal square root transformation. 

PowerTransformer() class in the python scikit library can be used for making these power transformations.

Data shown before and after log transformation: 

Data Preparation for Machine Learning ProjectsImage Source

Points to remember: 

  • Data transformations should be done on the training dataset, so that the statistic required for transformation is estimated from the training set only and then applied on the validation set. 
  • Decision trees and other tree-based ensembles like Random forest and boosting algorithms are not impacted by different scale of the input variables. Hence scaling may not be required.  
  • Linear regression and neural networks which use weighted sum of the input variables and K-nearest neighbors or SVM which compute distance or dot product between predictors will be impacted by the scale of the predictors, hence input variables should be scaled for these models. 
  • Between normalization and standardization, one should standardize when the data follows a Gaussian distribution, else normalize. 

Feature Engineering:  is the part of data pre-processing where we derive new features using one or more existing features. For e.g. when working on taxi fare prediction problem, we may derive a new feature, distance travelled in the ride with the use of latitude and longitude co-ordinates of the start and end point of the ride. Or when working on predicting sales or foot fall for a retail business we may need to add a new feature to factor in, the impact of holiday, weekends and festivals on the target variable. Hence, we may need to engineer these new predictors and feed them into our model to identify the underlying patterns effectively. 

Polynomial term: We may also add new features by raising the existing input variables to a higher degree polynomial. Polynomial terms help the model learn the non-linear patterns. When polynomial terms of existing features are added to the linear regression model, it is termed as polynomial regression. Usually, we stick to a smaller degree of 2 or 3. 

Interaction term: We may add new features that represent interaction between existing features by adding a product of two features. For e.g. if we are working on a problem to help businesses allocate their marketing budget between various marketing mediums like radio, TV and newspaper, we need to model how effective each medium is. We may like to factor in the interaction term of radio and newspaper campaign, to understand the effectiveness of marketing if both the radio and newspaper campaigns were run together at the same time. 

Similarly, when predicting a crop yield, we may engineer a new interaction term for fertilizer and water together to factor in how the yield varies when water and fertilizer are provided together. 

Points to remember: 

  • When using polynomial terms in the model, it is good practice to restrict the degree of the polynomial to 3 or at most 4. This is firstly, to control the number of input variables. Secondly, larger degree of the polynomial will result in large values which may impact the weights(parameters) to be large and hence make the model less sensitive to small changes. 
  • Domain knowledge or the advice of the SME may come in handy to identify effective interaction terms. 

Dimensionality Reduction: Sometimes data might have hundreds and even thousands of features. High dimensional data can be more complicated, with way more parameters to train and very complicated model structureIn higher dimensions, the volume of space is huge, and the data points become sparse, which could negatively impact the machine learning algorithm performance. This is sometimes also referred to as the curse of dimensionality.  

Dimensionality Reduction techniques are used to reduce the number of predictor variables in the dataset. Some techniques for dimensionality reduction are: 

  1. PCA or Principal Component Analysis uses linear algebra and Eigenvalue to achieve dimensionality reduction. For given datapoints PCA finds orthogonal set of directions, that have maximum variance. Rotating the reference frame, it finds the directions (ones which correspond to smallest eigen values) which can be neglected. 

Principal Component Analysis applied to a dataset is shown below: 

PCA or Principal Component Analysis

  1. Manifold learning is a non-linear dimensionality reduction technique which uses geometric properties of the data, to create low dimensional projections of a high dimensional data, while preserving its structure and relationships, and to visualize high dimensional data, which is otherwise difficult. SOM Self organizing Map also called Kohonen map and t-SNE are examples of Manifold learning techniques.  

t-distributed stochastic neighbor embedding (t-SNE) computes the probability that pairs of datapoints (in high dimension) are related and maps them in low dimension, such that data has a similar distribution. 

  1. Autoencoders are deep learning neural networks that learn low dimensional representation of a given dataset in an unsupervised manner. The hidden layer is limited to contain fewer neurons, thus it learns to map high dimensional input vector into low dimensional vector, while still preserving the underlying structure and relationships in the data. Autoencoders have two parts, encoder which learns to map high dimensional vector to a low-dimensional space and decoder, which maps the data from low to high dimension. The output from the encoder with reduced dimension can be fed into any another model for supervised learning. 

Points to remember:  

  • Dimensionality reduction is mostly performed after data cleaning and data scaling.  
  • It is imperative that the dimensionality reduction performed on the training data set must also be performed on the validation and the new data on which the model will predict. 

Conclusion:

Data preparation is an important and integral step of machine learning projects. There are multiple techniques for various data cleaning tasks. However, there are no best or worst data cleaning techniques. Every machine learning problem is unique and so is the underlying data. We need to apply different techniques and see what works best based on the data and the problem at hand.  

Suchita

Suchita Singh

Author

With 16+ years of experience, having served organisations like IBM for a decade, Suchita is currently playing the role of a data scientist at Algoritmo Lab with core hands-on with various tools and technologies and is helping lead a team of junior data scientists.

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Role of Unstructured Data in Data Science

Data has become the new game changer for businesses. Typically, data scientists categorize data into three broad divisions - structured, semi-structured, and unstructured data. In this article, you will get to know about unstructured data, sources of unstructured data, unstructured data vs. structured data, the use of structured and unstructured data in machine learning, and the difference between structured and unstructured data. Let us first understand what is unstructured data with examples. What is unstructured data? Unstructured data is a kind of data format where there is no organized form or type of data. Videos, texts, images, document files, audio materials, email contents and more are considered to be unstructured data. It is the most copious form of business data, and cannot be stored in a structured database or relational database. Some examples of unstructured data are the photos we post on social media platforms, the tagging we do, the multimedia files we upload, and the documents we share. Seagate predicts that the global data-sphere will expand to 163 zettabytes by 2025, where most of the data will be in the unstructured format. Characteristics of Unstructured DataUnstructured data cannot be organized in a predefined fashion, and is not a homogenous data model. This makes it difficult to manage. Apart from that, these are the other characteristics of unstructured data. You cannot store unstructured data in the form of rows and columns as we do in a database table. Unstructured data is heterogeneous in structure and does not have any specific data model. The creation of such data does not follow any semantics or habits. Due to the lack of any particular sequence or format, it is difficult to manage. Such data does not have an identifiable structure. Sources of Unstructured Data There are various sources of unstructured data. Some of them are: Content websites Social networking sites Online images Memos Reports and research papers Documents, spreadsheets, and presentations Audio mining, chatbots Surveys Feedback systems Advantages of Unstructured Data Unstructured data has become exceptionally easy to store because of MongoDB, Cassandra, or even using JSON. Modern NoSQL databases and software allows data engineers to collect and extract data from various sources. There are numerous benefits that enterprises and businesses can gain from unstructured data. These are: With the advent of unstructured data, we can store data that lacks a proper format or structure. There is no fixed schema or data structure for storing such data, which gives flexibility in storing data of different genres. Unstructured data is much more portable by nature. Unstructured data is scalable and flexible to store. Database systems like MongoDB, Cassandra, etc., can easily handle the heterogeneous properties of unstructured data. Different applications and platforms produce unstructured data that becomes useful in business intelligence, unstructured data analytics, and various other fields. Unstructured data analysis allows finding comprehensive data stories from data like email contents, website information, social media posts, mobile data, cache files and more. Unstructured data, along with data analytics, helps companies improve customer experience. Detection of the taste of consumers and their choices becomes easy because of unstructured data analysis. Disadvantages of Unstructured data Storing and managing unstructured data is difficult because there is no proper structure or schema. Data indexing is also a substantial challenge and hence becomes unclear due to its disorganized nature. Search results from an unstructured dataset are also not accurate because it does not have predefined attributes. Data security is also a challenge due to the heterogeneous form of data. Problems faced and solutions for storing unstructured data. Until recently, it was challenging to store, evaluate, and manage unstructured data. But with the advent of modern data analysis tools, algorithms, CAS (content addressable storage system), and big data technologies, storage and evaluation became easy. Let us first take a look at the various challenges used for storing unstructured data. Storing unstructured data requires a large amount of space. Indexing of unstructured data is a hectic task. Database operations such as deleting and updating become difficult because of the disorganized nature of the data. Storing and managing video, audio, image file, emails, social media data is also challenging. Unstructured data increases the storage cost. For solving such issues, there are some particular approaches. These are: CAS system helps in storing unstructured data efficiently. We can preserve unstructured data in XML format. Developers can store unstructured data in an RDBMS system supporting BLOB. We can convert unstructured data into flexible formats so that evaluating and storage becomes easy. Let us now understand the differences between unstructured data vs. structured data. Unstructured Data Vs. Structured Data In this section, we will understand the difference between structured and unstructured data with examples. STRUCTUREDUNSTRUCTUREDStructured data resides in an organized format in a typical database.Unstructured data cannot reside in an organized format, and hence we cannot store it in a typical database.We can store structured data in SQL database tables having rows and columns.Storing and managing unstructured data requires specialized databases, along with a variety of business intelligence and analytics applications.It is tough to scale a database schema.It is highly scalable.Structured data gets generated in colleges, universities, banks, companies where people have to deal with names, date of birth, salary, marks and so on.We generate or find unstructured data in social media platforms, emails, analyzed data for business intelligence, call centers, chatbots and so on.Queries in structured data allow complex joining.Unstructured data allows only textual queries.The schema of a structured dataset is less flexible and dependent.An unstructured dataset is flexible but does not have any particular schema.It has various concurrency techniques.It has no concurrency techniques.We can use SQL, MySQL, SQLite, Oracle DB, Teradata to store structured data.We can use NoSQL (Not Only SQL) to store unstructured data.Types of Unstructured Data Do you have any idea just how much of unstructured data we produce and from what sources? Unstructured data includes all those forms of data that we cannot actively manage in an RDBMS system that is a transactional system. We can store structured data in the form of records. But this is not the case with unstructured data. Before the advent of object-based storage, most of the unstructured data was stored in file-based systems. Here are some of the types of unstructured data. Rich media content: Entertainment files, surveillance data, multimedia email attachments, geospatial data, audio files (call center and other recorded audio), weather reports (graphical), etc., comes under this genre. Document data: Invoices, text-file records, email contents, productivity applications, etc., are included under this genre. Internet of Things (IoT) data: Ticker data, sensor data, data from other IoT devices come under this genre. Apart from all these, data from business intelligence and analysis, machine learning datasets, and artificial intelligence data training datasets are also a separate genre of unstructured data. Examples of Unstructured Data There are various sources from where we can obtain unstructured data. The prominent use of this data is in unstructured data analytics. Let us now understand what are some examples of unstructured data and their sources – Healthcare industries generate a massive volume of human as well as machine-generated unstructured data. Human-generated unstructured data could be in the form of patient-doctor or patient-nurse conversations, which are usually recorded in audio or text formats. Unstructured data generated by machines includes emergency video camera footage, surgical robots, data accumulated from medical imaging devices like endoscopes, laparoscopes and more.  Social Media is an intrinsic entity of our daily life. Billions of people come together to join channels, share different thoughts, and exchange information with their loved ones. They create and share such data over social media platforms in the form of images, video clips, audio messages, tagging people (this helps companies to map relations between two or more people), entertainment data, educational data, geolocations, texts, etc. Other spectra of data generated from social media platforms are behavior patterns, perceptions, influencers, trends, news, and events. Business and corporate documents generate a multitude of unstructured data such as emails, presentations, reports containing texts, images, presentation reports, video contents, feedback and much more. These documents help to create knowledge repositories within an organization to make better implicit operations. Live chat, video conferencing, web meeting, chatbot-customer messages, surveillance data are other prominent examples of unstructured data that companies can cultivate to get more insights into the details of a person. Some prominent examples of unstructured data used in enterprises and organizations are: Reports and documents, like Word files or PDF files Multimedia files, such as audio, images, designed texts, themes, and videos System logs Medical images Flat files Scanned documents (which are images that hold numbers and text – for example, OCR) Biometric data Unstructured Data Analytics Tools  You might be wondering what tools can come into use to gather and analyze information that does not have a predefined structure or model. Various tools and programming languages use structured and unstructured data for machine learning and data analysis. These are: Tableau MonkeyLearn Apache Spark SAS Python MS. Excel RapidMiner KNIME QlikView Python programming R programming Many cloud services (like Amazon AWS, Microsoft Azure, IBM Cloud, Google Cloud) also offer unstructured data analysis solutions bundled with their services. How to analyze unstructured data? In the past, the process of storage and analysis of unstructured data was not well defined. Enterprises used to carry out this kind of analysis manually. But with the advent of modern tools and programming languages, most of the unstructured data analysis methods became highly advanced. AI-powered tools use algorithms designed precisely to help to break down unstructured data for analysis. Unstructured data analytics tools, along with Natural language processing (NLP) and machine learning algorithms, help advanced software tools analyze and extract analytical data from the unstructured datasets. Before using these tools for analyzing unstructured data, you must properly go through a few steps and keep these points in mind. Set a clear goal for analyzing the data: It is essential to clear your intention about what insights you want to extract from your unstructured data. Knowing this will help you distinguish what type of data you are planning to accumulate. Collect relevant data: Unstructured data is available everywhere, whether it's a social media platform, online feedback or reviews, or a survey form. Depending on the previous point, that is your goal - you have to be precise about what data you want to collect in real-time. Also, keep in mind whether your collected details are relevant or not. Clean your data: Data cleaning or data cleansing is a significant process to detect corrupt or irrelevant data from the dataset, followed by modifying or deleting the coarse and sloppy data. This phase is also known as the data-preprocessing phase, where you have to reduce the noise, carry out data slicing for meaningful representation, and remove unnecessary data. Use Technology and tools: Once you perform the data cleaning, it is time to utilize unstructured data analysis tools to prepare and cultivate the insights from your data. Technologies used for unstructured data storage (NoSQL) can help in managing your flow of data. Other tools and programming libraries like Tableau, Matplotlib, Pandas, and Google Data Studio allows us to extract and visualize unstructured data. Data can be visualized and presented in the form of compelling graphs, plots, and charts. How to Extract information from Unstructured Data? With the growth in digitization during the information era, repetitious transactions in data cause data flooding. The exponential accretion in the speed of digital data creation has brought a whole new domain of understanding user interaction with the online world. According to Gartner, 80% of the data created by an organization or its application is unstructured. While extracting exact information through appropriate analysis of organized data is not yet possible, even obtaining a decent sense of this unstructured data is quite tough. Until now, there are no perfect tools to analyze unstructured data. But algorithms and tools designed using machine learning, Natural language processing, Deep learning, and Graph Analysis (a mathematical method for estimating graph structures) help us to get the upper hand in extracting information from unstructured data. Other neural network models like modern linguistic models follow unsupervised learning techniques to gain a good 'knowledge' about the unstructured dataset before going into a specific supervised learning step. AI-based algorithms and technologies are capable enough to extract keywords, locations, phone numbers, analyze image meaning (through digital image processing). We can then understand what to evaluate and identify information that is essential to your business. ConclusionUnstructured data is found abundantly from sources like documents, records, emails, social media posts, feedbacks, call-records, log-in session data, video, audio, and images. Manually analyzing unstructured data is very time-consuming and can be very boring at the same time. With the growth of data science and machine learning algorithms and models, it has become easy to gather and analyze insights from unstructured information.  According to some research, data analytics tools like MonkeyLearn Studio, Tableau, RapidMiner help analyze unstructured data 1200x faster than the manual approach. Analyzing such data will help you learn more about your customers as well as competitors. Text analysis software, along with machine learning models, will help you dig deep into such datasets and make you gain an in-depth understanding of the overall scenario with fine-grained analyses.
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Role of Unstructured Data in Data Science

Data has become the new game changer for busines... Read More

What Is Statistical Analysis and Its Business Applications?

Statistics is a science concerned with collection, analysis, interpretation, and presentation of data. In Statistics, we generally want to study a population. You may consider a population as a collection of things, persons, or objects under experiment or study. It is usually not possible to gain access to all of the information from the entire population due to logistical reasons. So, when we want to study a population, we generally select a sample. In sampling, we select a portion (or subset) of the larger population and then study the portion (or the sample) to learn about the population. Data is the result of sampling from a population.Major ClassificationThere are two basic branches of Statistics – Descriptive and Inferential statistics. Let us understand the two branches in brief. Descriptive statistics Descriptive statistics involves organizing and summarizing the data for better and easier understanding. Unlike Inferential statistics, Descriptive statistics seeks to describe the data, however, it does not attempt to draw inferences from the sample to the whole population. We simply describe the data in a sample. It is not developed on the basis of probability unlike Inferential statistics. Descriptive statistics is further broken into two categories – Measure of Central Tendency and Measures of Variability. Inferential statisticsInferential statistics is the method of estimating the population parameter based on the sample information. It applies dimensions from sample groups in an experiment to contrast the conduct group and make overviews on the large population sample. Please note that the inferential statistics are effective and valuable only when examining each member of the group is difficult. Let us understand Descriptive and Inferential statistics with the help of an example. Task – Suppose, you need to calculate the score of the players who scored a century in a cricket tournament.  Solution: Using Descriptive statistics you can get the desired results.   Task – Now, you need the overall score of the players who scored a century in the cricket tournament.  Solution: Applying the knowledge of Inferential statistics will help you in getting your desired results.  Top Five Considerations for Statistical Data AnalysisData can be messy. Even a small blunder may cost you a fortune. Therefore, special care when working with statistical data is of utmost importance. Here are a few key takeaways you must consider to minimize errors and improve accuracy. Define the purpose and determine the location where the publication will take place.  Understand the assets to undertake the investigation. Understand the individual capability of appropriately managing and understanding the analysis.  Determine whether there is a need to repeat the process.  Know the expectation of the individuals evaluating reviewing, committee, and supervision. Statistics and ParametersDetermining the sample size requires understanding statistics and parameters. The two being very closely related are often confused and sometimes hard to distinguish.  StatisticsA statistic is merely a portion of a target sample. It refers to the measure of the values calculated from the population.  A parameter is a fixed and unknown numerical value used for describing the entire population. The most commonly used parameters are: Mean Median Mode Mean :  The mean is the average or the most common value in a data sample or a population. It is also referred to as the expected value. Formula: Sum of the total number of observations/the number of observations. Experimental data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20  Calculating mean:   (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20)/10  = 110/10   = 11 Median:  In statistics, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. It’s the mid-value obtained by arranging the data in increasing order or descending order. Formula:  Let n be the data set (increasing order) When data set is odd: Median = n+1/2th term Case-I: (n is odd)  Experimental data set = 1, 2, 3, 4, 5  Median (n = 5) = [(5 +1)/2]th term      = 6/2 term       = 3rd term   Therefore, the median is 3 When data set is even: Median = [n/2th + (n/2 + 1)th] /2 Case-II: (n is even)  Experimental data set = 1, 2, 3, 4, 5, 6   Median (n = 6) = [n/2th + (n/2 + 1)th]/2     = ( 6/2th + (6/2 +1)th]/2     = (3rd + 4th)/2      = (3 + 4)/2      = 7/2      = 3.5  Therefore, the median is 3.5 Mode: The mode is the value that appears most often in a set of data or a population. Experimental data set= 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4,4,5, 6  Mode = 3 (Since 3 is the most repeated element in the sequence.) Terms Used to Describe DataWhen working with data, you will need to search, inspect, and characterize them. To understand the data in a tech-savvy and straightforward way, we use a few statistical terms to denote them individually or in groups.  The most frequently used terms used to describe data include data point, quantitative variables, indicator, statistic, time-series data, variable, data aggregation, time series, dataset, and database. Let us define each one of them in brief: Data points: These are the numerical files formed and organized for interpretations. Quantitative variables: These variables present the information in digit form.  Indicator: An indicator explains the action of a community's social-economic surroundings.  Time-series data: The time-series defines the sequential data.  Data aggregation: A group of data points and data set. Database: A group of arranged information for examination and recovery.  Time-series: A set of measures of a variable documented over a specified time. Step-by-Step Statistical Analysis ProcessThe statistical analysis process involves five steps followed one after another. Step 1: Design the study and find the population of the study. Step 2: Collect data as samples. Step 3: Describe the data in the sample. Step 4: Make inferences with the help of samples and calculations Step 5: Take action Data distributionData distribution is an entry that displays entire imaginable readings of data. It shows how frequently a value occurs. Distributed data is always in ascending order, charts, and graphs enabling visibility of measurements and frequencies. The distribution function displaying the density of values of reading is known as the probability density function. Percentiles in data distributionA percentile is the reading in a distribution with a specified percentage of clarifications under it.  Let us understand percentiles with the help of an example.  Suppose you have scored 90th percentile on a math test. A basic interpretation is that merely 4-5% of the scores were higher than your scores. Right? The median is 50th percentile because the assumed 50% of the values are higher than the median. Dispersion Dispersion explains the magnitude of distribution readings anticipated for a specific variable and multiple unique statistics like range, variance, and standard deviation. For instance, high values of a data set are widely scattered while small values of data are firmly clustered. Histogram The histogram is a pictorial display that arranges a group of data facts into user detailed ranges. A histogram summarizes a data series into a simple interpreted graphic by obtaining many data facts and combining them into reasonable ranges. It contains a variety of results into columns on the x-axis. The y axis displays percentages of data for each column and is applied to picture data distributions. Bell Curve distribution Bell curve distribution is a pictorial representation of a probability distribution whose fundamental standard deviation obtained from the mean makes the bell, shaped curving. The peak point on the curve symbolizes the maximum likely occasion in a pattern of data. The other possible outcomes are symmetrically dispersed around the mean, making a descending sloping curve on both sides of the peak. The curve breadth is therefore known as the standard deviation. Hypothesis testingHypothesis testing is a process where experts experiment with a theory of a population parameter. It aims to evaluate the credibility of a hypothesis using sample data. The five steps involved in hypothesis testing are:  Identify the no outcome hypothesis.  (A worthless or a no-output hypothesis has no outcome, connection, or dissimilarities amongst many factors.) Identify the alternative hypothesis.  Establish the importance level of the hypothesis.  Estimate the experiment statistic and equivalent P-value. P-value explains the possibility of getting a sample statistic.  Sketch a conclusion to interpret into a report about the alternate hypothesis. Types of variablesA variable is any digit, amount, or feature that is countable or measurable. Simply put, it is a variable characteristic that varies. The six types of variables include the following: Dependent variableA dependent variable has values that vary according to the value of another variable known as the independent variable.  Independent variableAn independent variable on the other side is controllable by experts. Its reports are recorded and equated.  Intervening variableAn intervening variable explicates fundamental relations between variables. Moderator variableA moderator variable upsets the power of the connection between dependent and independent variables.  Control variableA control variable is anything restricted to a research study. The values are constant throughout the experiment. Extraneous variableExtraneous variable refers to the entire variables that are dependent but can upset experimental outcomes. Chi-square testChi-square test records the contrast of a model to actual experimental data. Data is unsystematic, underdone, equally limited, obtained from independent variables, and a sufficient sample. It relates the size of any inconsistencies among the expected outcomes and the actual outcomes, provided with the sample size and the number of variables in the connection. Types of FrequenciesFrequency refers to the number of repetitions of reading in an experiment in a given time. Three types of frequency distribution include the following: Grouped, ungrouped Cumulative, relative Relative cumulative frequency distribution. Features of FrequenciesThe calculation of central tendency and position (median, mean, and mode). The measure of dispersion (range, variance, and standard deviation). Degree of symmetry (skewness). Peakedness (kurtosis). Correlation MatrixThe correlation matrix is a table that shows the correlation coefficients of unique variables. It is a powerful tool that summarises datasets points and picture sequences in the provided data. A correlation matrix includes rows and columns that display variables. Additionally, the correlation matrix exploits in aggregation with other varieties of statistical analysis. Inferential StatisticsInferential statistics use random data samples for demonstration and to create inferences. They are measured when analysis of each individual of a whole group is not likely to happen. Applications of Inferential StatisticsInferential statistics in educational research is not likely to sample the entire population that has summaries. For instance, the aim of an investigation study may be to obtain whether a new method of learning mathematics develops mathematical accomplishment for all students in a class. Marketing organizations: Marketing organizations use inferential statistics to dispute a survey and request inquiries. It is because carrying out surveys for all the individuals about merchandise is not likely. Finance departments: Financial departments apply inferential statistics for expected financial plan and resources expenses, especially when there are several indefinite aspects. However, economists cannot estimate all that use possibility. Economic planning: In economic planning, there are potent methods like index figures, time series investigation, and estimation. Inferential statistics measures national income and its components. It gathers info about revenue, investment, saving, and spending to establish links among them. Key TakeawaysStatistical analysis is the gathering and explanation of data to expose sequences and tendencies.   Two divisions of statistical analysis are statistical and non-statistical analyses.  Descriptive and Inferential statistics are the two main categories of statistical analysis. Descriptive statistics describe data, whereas Inferential statistics equate dissimilarities between the sample groups.  Statistics aims to teach individuals how to use restricted samples to generate intellectual and precise results for a large group.   Mean, median, and mode are the statistical analysis parameters used to measure central tendency.   Conclusion Statistical analysis is the procedure of gathering and examining data to recognize sequences and trends. It uses random samples of data obtained from a population to demonstrate and create inferences on a group. Inferential statistics applies economic planning with potent methods like index figures, time series investigation, and estimation.  Statistical analysis finds its applications in all the major sectors – marketing, finance, economic, operations, and data mining. Statistical analysis aids marketing organizations in disputing a survey and requesting inquiries concerning their merchandise. 
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What Is Statistical Analysis and Its Business Appl...

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Measures of Dispersion: All You Need to Know

What is Dispersion in StatisticsDispersion in statistics is a way of describing how spread out a set of data is. Dispersion is the state of data getting dispersed, stretched, or spread out in different categories. It involves finding the size of distribution values that are expected from the set of data for the specific variable. The statistical meaning of dispersion is “numeric data that is likely to vary at any instance of average value assumption”.Dispersion of data in Statistics helps one to easily understand the dataset by classifying them into their own specific dispersion criteria like variance, standard deviation, and ranging.Dispersion is a set of measures that helps one to determine the quality of data in an objectively quantifiable manner.The measure of dispersion contains almost the same unit as the quantity being measured. There are many Measures of Dispersion found which help us to get more insights into the data: Range Variance Standard Deviation Skewness IQR  Image SourceTypes of Measure of DispersionThe Measure of Dispersion is divided into two main categories and offer ways of measuring the diverse nature of data. It is mainly used in biological statistics. We can easily classify them by checking whether they contain units or not. So as per the above, we can divide the data into two categories which are: Absolute Measure of Dispersion Relative Measure of DispersionAbsolute Measure of DispersionAbsolute Measure of Dispersion is one with units; it has the same unit as the initial dataset. Absolute Measure of Dispersion is expressed in terms of the average of the dispersion quantities like Standard or Mean deviation. The Absolute Measure of Dispersion can be expressed  in units such as Rupees, Centimetre, Marks, kilograms, and other quantities that are measured depending on the situation. Types of Absolute Measure of Dispersion: Range: Range is the measure of the difference between the largest and smallest value of the data variability. The range is the simplest form of Measure of Dispersion. Example: 1,2,3,4,5,6,7 Range = Highest value – Lowest value   = ( 7 – 1 ) = 6 Mean (μ): Mean is calculated as the average of the numbers. To calculate the Mean, add all the outcomes and then divide it with the total number of terms. Example: 1,2,3,4,5,6,7,8 Mean = (sum of all the terms / total number of terms)                = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8                = 36 / 8                = 4.5 Variance (σ2): In simple terms, the variance can be calculated by obtaining the sum of the squared distance of each term in the distribution from the Mean, and then dividing this by the total number of the terms in the distribution.  It basically shows how far a number, for example, a student’s mark in an exam, is from the Mean of the entire class. Formula: (σ2) = ∑ ( X − μ)2 / N Standard Deviation: Standard Deviation can be represented as the square root of Variance. To find the standard deviation of any data, you need to find the variance first. Formula: Standard Deviation = √σ Quartile: Quartiles divide the list of numbers or data into quarters. Quartile Deviation: Quartile Deviation is the measure of the difference between the upper and lower quartile. This measure of deviation is also known as interquartile range. Formula: Interquartile Range: Q3 – Q1. Mean deviation: Mean Deviation is also known as an average deviation; it can be computed using the Mean or Median of the data. Mean deviation is represented as the arithmetic deviation of a different item that follows the central tendency. Formula: As mentioned, the Mean Deviation can be calculated using Mean and Median. Mean Deviation using Mean: ∑ | X – M | / N Mean Deviation using Median: ∑ | X – X1 | / N Relative Measure of DispersionRelative Measures of dispersion are the values without units. A relative measure of dispersion is used to compare the distribution of two or more datasets.  The definition of the Relative Measure of Dispersion is the same as the Absolute Measure of Dispersion; the only difference is the measuring quantity.  Types of Relative Measure of Dispersion: Relative Measure of Dispersion is the calculation of the co-efficient of Dispersion, where 2 series are compared, which differ widely in their average.  The main use of the co-efficient of Dispersion is when 2 series with different measurement units are compared.  1. Co-efficient of Range: it is calculated as the ratio of the difference between the largest and smallest terms of the distribution, to the sum of the largest and smallest terms of the distribution.  Formula: L – S / L + S  where L = largest value S= smallest value 2. Co-efficient of Variation: The coefficient of variation is used to compare the 2 data with respect to homogeneity or consistency.  Formula: C.V = (σ / X) 100 X = standard deviation  σ = mean 3. Co-efficient of Standard Deviation: The co-efficient of Standard Deviation is the ratio of standard deviation with the mean of the distribution of terms.  Formula: σ = ( √( X – X1)) / (N - 1) Deviation = ( X – X1)  σ = standard deviation  N= total number  4. Co-efficient of Quartile Deviation: The co-efficient of Quartile Deviation is the ratio of the difference between the upper quartile and the lower quartile to the sum of the upper quartile and lower quartile.  Formula: ( Q3 – Q3) / ( Q3 + Q1) Q3 = Upper Quartile  Q1 = Lower Quartile 5. Co-efficient of Mean Deviation: The co-efficient of Mean Deviation can be computed using the mean or median of the data. Mean Deviation using Mean: ∑ | X – M | / N Mean Deviation using Mean: ∑ | X – X1 | / N Why dispersion is important in a statisticThe knowledge of dispersion is vital in the understanding of statistics. It helps to understand concepts like the diversification of the data, how the data is spread, how it is maintained, and maintaining the data over the central value or central tendency. Moreover, dispersion in statistics provides us with a way to get better insights into data distribution. For example,  3 distinct samples can have the same Mean, Median, or Range but completely different levels of variability. How to Calculate DispersionDispersion can be easily calculated using various dispersion measures, which are already mentioned in the types of Measure of Dispersion described above. Before measuring the data, it is important to understand the diversion of the terms and variation. One can use the following method to calculate the dispersion: Mean Standard deviation Variance Quartile deviation For example, let us consider two datasets: Data A:97,98,99,100,101,102,103  Data B: 70,80,90,100,110,120,130 On calculating the mean and median of the two datasets, both have the same value, which is 100. However, the rest of the dispersion measures are totally different as measured by the above methods.  The range of B is 10 times higher, for instance. How to represent Dispersion in Statistics Dispersion in Statistics can be represented in the form of graphs and pie-charts. Some of the different ways used include: Dot Plots Box Plots Stems Leaf Plots Example: What is the variance of the values 3,8,6,10,12,9,11,10,12,7?  Variation of the values can be calculated using the following formula: (σ2) = ∑ ( X − μ)2 / N (σ2) = 7.36 What is an example of dispersion? One of the examples of dispersion outside the world of statistics is the rainbow- where white light is split into 7 different colours separated via wavelengths.  Some statistical ways of measuring it are- Standard deviation Range Mean absolute difference Median absolute deviation Interquartile change Average deviation Conclusion: Dispersion in statistics refers to the measure of variability of data or terms. Such variability may give random measurement errors where some of the instrumental measurements are found to be imprecise. It is a statistical way of describing how the terms are spread out in different data sets. The more sets of values, the more scattered data is found, and it is always directly proportional. This range of values can vary from 5 - 10 values to 1000 - 10,000 values. This spread of data is described by the range of descriptive range of statistics. The dispersion in statistics can be represented using a Dot Plot, Box Plot, and other different ways. 
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Measures of Dispersion: All You Need to Know

What is Dispersion in StatisticsDispersion in stat... Read More