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Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build 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 Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Using statistics: How to understand population distributions?

Kunal Jain
Kunal Jain 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.

histogrammeanmedianmodestandard deciationstatistics
Kunal Jain
Kunal Jain

Kunal Jain is the Founder and CEO of Analytics Vidhya, one of the world's leading communities of Al professionals. With over 17 years of experience in the field, Kunal has been instrumental in shaping the global Al landscape. His expertise spans diverse markets, from developed economies like the UK to emerging ones like India, where he has successfully led and delivered complex data-driven solutions. As a recognized thought leader, Kunal has empowered countless individuals to realize their Al ambitions through his visionary approach to Al education and community building. Before founding Analytics Vidhya, Kunal earned both his undergraduate and postgraduate degrees from IIT Bombay and held key roles at Capital One and Aviva Life Insurance across multiple geographies. His passion lies at the intersection of analytics, Al, and fostering a thriving community of data science professionals.

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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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