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Machine Learning Basics for a Newbie
6 Steps of Machine learning LifecycleIntroduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data InsightsDescriptive StatisticsInferential StatisticsHow to Understand Population Distributions?
Reading Data Files into PythonDifferent Variable Datatypes
Probability for Data ScienceBasic Concepts of ProbabilityAxioms of ProbabilityConditional Probability
Central Tendencies for Continuous VariablesSpread of DataKDE plots for Continuous VariableOverview of Distribution for Continuous variablesNormal DistributionSkewed DistributionSkeweness and KurtosisDistribution for Continuous Variable
Central Tendencies for Categorical VariablesUnderstanding Discrete DistributionsPerforming EDA on Categorical Variables
Dealing with Missing ValuesUnderstanding OutliersIdentifying Outliers in DataOutlier Detection in PythonOutliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and PopulationCentral Limit TheoremConfidence Interval and Margin of Error
Bivariate Analysis Introduction
CovariancePearson CorrelationSpearman's Correlation & Kendall's TauCorrelation versus CausationTabular and Graphical methods for Bivariate AnalysisPerforming Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical VariablesIntroduction to Hypothesis TestingP-valueTwo sample Z-testT-testT-test vs Z-testPerforming Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares TestBivariate Analysis on Categorical Categorical Variables
Multivariate AnalysisA Comprehensive Guide to Data ExplorationThe Data Science behind IPL
Supervised Learning vs Unsupervised LearningReinforcement LearningGenerative and Descriminative ModelsParametric and Non Parametric model
Machine Learning PipelinePreparing DatasetBuild a Benchmark Model: RegressionBuild a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should knowConfusion MatrixAccuracyPrecision and RecallAUC-ROCLog LossR2 and Adjusted R2
Dealing with Missing ValuesReplacing Missing ValuesImputing Missing Values in DataWorking with Categorical VariablesWorking with OutliersPreprocessing Data for Model Building
Understanding Cost FunctionUnderstanding Gradient DescentMath Behind Gradient DescentAssumptions of Linear RegressionImplement Linear Regression from ScratchTrain Linear Regression in PythonImplementing Linear Regression in RDiagnosing Residual Plots in Linear Regression ModelsGeneralized Linear ModelsIntroduction to Logistic RegressionOdds RatioImplementing Logistic Regression from ScratchIntroduction to Scikit-learn in PythonTrain Logistic Regression in pythonMulticlass using Logistic RegressionHow to use Multinomial and Ordinal Logistic Regression in R ?Challenges with Linear RegressionIntroduction to RegularisationImplementing RegularisationRidge RegressionLasso Regression
Introduction to K Nearest NeighboursDetermining the Right Value of K in KNNImplement KNN from ScratchImplement KNN in Python
Bias Variance TradeoffIntroduction to Overfitting and UnderfittingVisualizing Overfitting and UnderfittingSelecting the Right ModelWhat is Validation?Hold-Out ValidationUnderstanding K Fold Cross Validation
Introduction to Feature SelectionFeature Selection AlgorithmsMissing Value RatioLow Variance FilterHigh Correlation FilterBackward Feature EliminationForward Feature SelectionImplement Feature Selection in PythonImplement Feature Selection in R
Introduction to Decision TreePurity in Decision TreeTerminologies Related to Decision TreeHow to Select Best Split Point in Decision Tree?Chi-SquaresInformation GainReduction in VarianceOptimizing Performance of Decision TreeTrain Decision Tree using Scikit LearnPruning of Decision Trees
Introduction to Feature EngineeringFeature TransformationFeature ScalingFeature EngineeringFrequency EncodingAutomated Feature Engineering: Feature Tools
Introduction to Naive BayesConditional Probability and Bayes TheoremIntroduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings!Working of Naive BayesMath behind Naive BayesTypes of Naive BayesImplementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification ProblemEvaluation Metrics: Multi Class Classification
Introduction to Ensemble TechniquesBasic Ensemble TechniquesImplementing Basic Ensemble TechniquesFinding Optimal Weights of Ensemble Learner using Neural NetworkWhy Ensemble Models Work well?
Introduction to StackingImplementing StackingVariants of StackingImplementing Variants of StackingIntroduction to BlendingBootstrap SamplingIntroduction to Random SamplingHyper-parameters of Random ForestImplementing Random ForestOut-of-Bag (OOB) Score in the Random ForestIPL Team Win Prediction Project Using Machine LearningIntroduction to BoostingGradient Boosting AlgorithmMath behind GBMImplementing GBM in pythonRegularized Greedy ForestsExtreme Gradient BoostingImplementing XGBM in pythonTuning Hyperparameters of XGBoost in PythonImplement XGBM in R/H2OAdaptive BoostingImplementing Adaptive BoosingLightGBMImplementing LightGBM in PythonCatboostImplementing Catboost in Python
Different Hyperparameter Tuning methodsImplementing Different Hyperparameter Tuning methodsGridsearchCVRandomizedsearchCVBayesian Optimization for Hyperparameter TuningHyperopt
Understanding SVM AlgorithmSVM Kernels In-depth Intuition and Practical ImplementationSVM Kernel TricksKernels and Hyperparameters in SVMImplementing SVM from Scratch in Python and R
Introduction to Principal Component AnalysisSteps to Perform Principal Compound AnalysisComputation of Covariance MatrixFinding Eigenvectors and EigenvaluesImplementing PCA in pythonVisualizing PCAA Brief Introduction to Linear Discriminant AnalysisIntroduction to Factor Analysis
Introduction to ClusteringApplications of ClusteringEvaluation Metrics for ClusteringUnderstanding K-MeansImplementation of K-Means in PythonImplementation of K-Means in RChoosing Right Value for KProfiling Market Segments using K-Means ClusteringHierarchical ClusteringImplementation of Hierarchial ClusteringDBSCANDefining Similarity between clustersBuild Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to DaskWorking with CuML
Introduction to Machine Learning InterpretabilityFramework and Interpretable Modelsmodel Agnostic Methods for InterpretabilityImplementing Interpretable ModelUnderstanding SHAPOut-of-Core MLIntroduction to Interpretable Machine Learning ModelsModel Agnostic Methods for InterpretabilityGame Theory & Shapley Values
Introduction to AutoMLImplementation of MLBoxIntroduction to PyCaretTPOTAuto-SklearnEvalML
Pickle and JoblibIntroduction to Model Deployment
Deploying Machine Learning Model using StreamlitDeploying ML Models in DockerDeploy Using StreamlitDeploy on HerokuDeploy Using NetlifyIntroduction to Amazon SagemakerSetting up Amazon SageMakerUsing SageMaker Endpoint to Generate InferenceDeploy on Microsoft Azure CloudIntroduction to Flask for ModelDeploying ML model using Flask
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Using statistics: How to understand population distributions?

kunal
kunal Last Updated : 17 Apr, 2015
5 min read

One of the common queries, which I get on the blog is:

I am not a Mathematics / Statistics graduate. Can I still become a good business analyst?

or

I am not good at statistics. Can I still change my career to become a business analyst?

The simple answer to the question is – you can’t become a good analyst until you know statistics. However, you don’t need to be an expert in statistics to become a good business analyst.

So, you don’t need to understand the joke in the strip, in order to qualify as a business analyst:

xkcd_seashell

 

Two types of Business Analytics:

Business anlaytics can be divided in two classes – applied business analytics and theoretical business analytics. Here are definitions of the two streams:

  1. Applied Business Analytics – This is the work, where the emphasis is to solve a problem at hand. What matters is that you have a strategy / algorithm, which is better than what is happening currently. You deal with practical problems in this stream – messy data, missing values, bad data capture etc. More than 95% of times, you would typically use the algorithm and outputs straight from the tools. As long as you are aware of the assumptions in your model, can check whether they are holding good and interpret the output of the algorithms correctly, you are good for applied business analytics.
    • For example, if you know the assumptions in Linear regression and can interpret what is R-square and adjusted R-square, you would be good to apply Linear Regression.
  2. Theoretical Business Analytics – This is the research area in business analytics. When you have a problem, where current set of algorithms are already optimized and applying standard techniques would not provide you any further uplift. This is when, you need to get into statistical details of various algorithms and then improve them.

categories of business analytics

 

Please note that this is not a standard categorization of Business Analytics and it might be difficult to identify some projects in exact buckets. However, it is good enough to communicate the point that you can deal with most of the business analytics problems with basic knowledge of statistics.

What does an analyst need to know?

Now, that you understand the two classes of business analytics, here is some good news! You don’t need to be a statistician to practice applied business analytics.

So, what exactly do you need to know to become an applied business analytics practitioner? I thought why not run a series of articles explaining the basic concepts of statistics, an applied BA practitioner needs to know.

Please note that this series is not intended to be a thesis on statistics. Instead, it takes a very practical outlook to apply statistics to solve business problems.

 

Concepts to understand population distributions:

One of the first things a business analyst needs to do is understand various distributions of parameters and population.

One of the most frequently used method to understand distributions is to plot them using histograms. A histogram represents frequencies of various values through a plot in uniform buckets (popularly known as bins). In case of continuous variables, a histogram represents the probability distribution function (we will cover this later). If you want an example of how histogram is plotted, you can look at this video from Khanacademy. Here is how a typical histogram might look like:

Example of histogram. Source: Wikipedia

Example of histogram. Source: Wikipedia

There are 3 variety of measures, required to understand a distribution:

  • Measure of Central tendency
  • Measure of dispersion
  • Measure to describe shape of curve

Measures of Central tendency:

Measures of central tendencies are measures, which help you describe a population, through a single metric. For example, if you were to compare Saving habits of people across various nations, you will compare average Savings rate in each of these nations.

Following are the measures of central tendency:

  • Mean – or the average
  • Median – the value, which divides the population in two half
  • Mode – the most frequent value in a population

The following image illustrates how mean, median and mode would be placed in a couple of scenarios:

central_tendency

Among the three measures, mean is typically affected the most by Outliers (unusually high or low values), followed by the median and mode.

Measures of Dispersion:

Measures of dispersion reveal how is the population distributed around the measures of central tendency.

  • Range – Difference in the maximum and minimum value in the population
  • Quartiles – Values, which divide the populaiton in 4 equal subsets (typically referred to as first quartile, second quartile and third quartile)
  • Inter-quartile range – The difference in third quartile (Q3) and first quartile (Q1). By definition of quartiles, 50% of the population lies in the inter-quartile range.
  • Variance: The average of the squared differences from the Mean.
  • Standard Deviation: is square root of Variance
standard_deviation

Difference in distribution of 2 populations with same mean, median and mode. Source: Wikipedia

 

Measures to describe shape of distribution:

  • Skewness – Skewness is a measure of the asymmetry. Negatively skewed curve has a long left tail and vice versa.
  • Kurtosis – Kurtosis is a measure of the “peaked ness”. Distributions with higher peaks have positive kurtosis and vice-versa

skewness and kurtosis

 

A few practical tips to understand distributions better:

  • Use of box plots: Box plots are one of the easiest and most intuitive way to understand distributions. They show mean, median, quartiles and Outliers on single plot.

box plot

  • You can use box plots next to each other for various categories / segments of population to understand overlap / differences in the population. Following is an example of one such comparison (with illustrative data):

box_plot_comparisonIn this post, we looked use of statistics to plot and understand distributions of populations – first steps for any business analyst to do in a project. In the articles to follow in this series, we will look at use of confidence intervals, hypothesis testing, probabilities and measures to judge various predictive models. If you would want me to cover more topics, please let me know through comments below.

In the article next week (from baby steps in Python series), we will see how to look at these measures and distributions using Python on a Kaggle dataset.

If you like what you just read & want to continue your analytics learning, subscribe to our emails, follow us on twitter or like our facebook page.

kunal
kunal

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Responses From Readers

Clear

Shreenag Haranhalli
Shreenag Haranhalli

Thank you for a lovely insight . I have just started my career as a data analyst so i would like to ask you are there any books or courses that i can do to enhance my statistics skills ?

123

Chirag Pradhan
Chirag Pradhan

Precise and to the point. Your blog is such a treasure trove. Looking forward to read more on this topic. Thanks Kunal

123

Parul
Parul

Thanks Kunal, helpful article, Can you explain same things using SAS ? If possible, please explain a bit more about kurtosis and what is the physical significance of it along with skewness ? Also, by looking at default output of means procedure in SAS, what story can we tell to the client ? Can you please answer this to make me understand how to interpret the results. I know we get N, min, max, std and mean as default but how to tell a story using these to the third person is what I want to understand . Any enlightment would be of great help.

123

Kunal Jain
Kunal Jain

Parul, Getting the output from SAS is very easy, you can use proc means and proc univariate. With regards to the story, stay tuned for the next article. Regards, Kunal

123

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