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Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
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
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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
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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
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8 Ways to Improve Accuracy of Machine Learning Models
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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

The Measure of Central Tendencies in Statistics -A Beginner’s Guide

Shrish
Shrish Last Updated : 08 Jul, 2021
5 min read

This article was published as a part of the Data Science Blogathon

Statistics. Whenever I hear this term, I imagine of below

statistics | measure of central tendencies
Image is taken from www. mathnstuff.com

Looks pretty scary to me. In this blog, my aim is to introduce you to the measure of central tendency used in statistics in the easiest possible way. So, let’s get started.

Interesting Sidenote

Before starting with the measure of central tendency, let me share an interesting side note. Do you know these measures of central tendency were used way back during world war 1 and world war 2?.

To be precise, these measures were used in order to access the damage that happened to aircraft during dogfights. In addition to that, those measures were used to also assess the return of aircraft at the rendezvous points. Interesting isn’t it.

aircraft damage
Aircraft damage using world war 1 – Image is taken from www.theatlantic.com

Population and Sample

Before we start with a measure of central tendencies, we need to understand few core concepts. One of them being population and sample.

Population

From a definition viewpoint, the population is a collection of all data points of interest. Let’s get an understanding of this with the help of an example.

Example:- Let’s say we are conducting a survey. Our aim to find out the total number of employees an organization is having. In this case, the total number of employees in the organization is known as population.

Sample

From a definition viewpoint, a sample is a subset of the population. Let’s get an understanding of this with the help of an example.

Example:- Let’s say we are conducting a survey. Our aim to find out the total number of employees on a particular project. In this case, the total number of employees in a project is known as a sample.

Population vs sample | measure of central tendencies
Population Vs Sample – Image is taken from Scribbr.com

What to chose between Population and Sample?

Well in most of the real-life case scenarios, we always deal with sample data. The reason behind this is that a sample is easy to collect and easier to compute than the population. Based on the result that we obtained for a sample, we can then use predictive analytics to make predictions about the entire population.

Parameter and Statistic

Now we have a core understanding of the difference between population and sample. Let’s quickly cover two more important concepts in this aspect – Parameter and Statistic

Parameter

From a definition viewpoint, numbers that are obtained when working with a population are known as a parameter.

Example:- Let’s consider the same example where we are going to count the total number of employees working in an organization. After completion of our survey, we arrive at number – 20000. In this context, 20000 is known as a parameter.

Statistic

From a definition viewpoint, numbers that are obtained when working with a sample is known as a statistic.

Example:- Let’s consider the same example where we are going to count the total number of employees working on a particular project. After completion of our survey, we arrive at number – 20. In this context, 20 is known as a statistic.

That’s why statistics is called statistics !!

Parameter vs statistics
Parameters Vs Statistics – Image is taken from dummies.com

The Measure of Central tendency

Now we have a core understanding of population and sample and their mapping with parameters and statistics. Before starting with our main topic, you might have a query – “What is meant by Central Tendency ?”.

Well, the concept of central tendency is based on the below fact –

“Provided with a larger number of observations of similar type, most of the observations seems to cluster around central position when represented as a graph”.

 

central tendency
Central Tendency – Image is taken from dummies.com

As we can see in the above graph, most of the observation tends to cluster around the central position and hence the term central tendency.

Now let’s start with the measure of central tendencies.

Mean

This is the very first measure of central tendency. Mean also known as the arithmetic mean is the statistical average of all data points in question.

Example :- Let’s consider first 10 natural numbers – 1,2,3,4,5,6,7,8,9,10

In this case, the mean will be the sum of all those numbers divided by the total number of numbers in questions.

( 1+2+3+4+5+6+7+8+9+10)/10 = 5.5

Advantages of mean:

1.Easiest measure of central tendency

2.Easier to compute

Disadvantages of mean:

1.Heavily affected  by the presence of outlier

You might have a question here – “What is an outlier?”

Outlier is basically a data point that is significantly different from the rest of the data points in consideration. So if a dataset is having extremely high or extremely low value, that might be considered as an outlier. There are multiple techniques to detect the presence of outliers like Box plot, five-number summary, etc. but those concepts are out of the scope of this article.

Example:- Let say we have 10 people in a room. Our aim is to compute the average salary of all people in a room. It will be computed by adding the salaries of all people divided by the total number of people. Now imagine Jeff Bezos walked into our room and now if we compute our mean, it is going to be significantly different than previously computed. The reason being the presence of an outlier ( Jeff Bezos in this case since he is having an extremely high salary ).

Median

This is the second measure of central tendency. Median is basically the middlemost data point in the dataset when arranged in ascending or descending order.

In this aspect, there are two variations of the median.

Median with even number of data points

If there are an even number of observations or data points, then the median is simply the average of the middle two numbers.

Example :- Let’s consider first 10 natural numbers – 1,2,3,4,5,6,7,8,9,10

In this case, the median will be the average of the middle two numbers which is going to be 5.5

Median with an odd number of data points

If there are an odd number of observations or data points, then the median is simply the middlemost observation.

Example :- Let’s consider first 11 natural numbers – 1,2,3,4,5,6,7,8,9,10,11

In this case, the median will be the middlemost observation which is going to be 6 in this case.

Advantages of median:

1.Higher resistance to outlier as compared to mean

Disadvantages of median:

1.Data needs to be ordered either in ascending or descending order

Mode

This is the third and last measure of central tendency. Mode is basically the value that appears the most in the dataset.

Example:- Let’s say we have following numbers – 1,2,3,4,4,4,4,4,4,5,6,7,8,9

Here we can clearly see that number 4 is repeated the most number of times and hence going to be mode in this case.

Advantages of mode:

1.Higher resistance to outlier as compared to mean and median

Disadvantages of mode:

1.Difficult to determine if data has more than 1 mode

Hope you like this blog on measures of central tendency.

LinkedIn:

https://www.linkedin.com/in/shrish-mohadarkar-060209109/

The media shown in this article are not owned by Analytics Vidhya and are used at the Author’s discretion.
blogathonCentral Tendencystatistics
Shrish
Shrish

My name is Shrish. I have been working as a data scientist at EY. I love technology and during my free time, I try to use my skills to create something awesome in python so that it can be shared on the analyticsvidhya platform

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AUWAL ALIYU YABO
AUWAL ALIYU YABO

I really appreciate with your efforts, may the almighty Allah reward you abundantly.

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Shamim

Good to some extent, but honestly there was nothing to learn......

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Thank you so much Very good and informative topics discussed

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Mean, Mode and Median – Measures of Central Tendency
Mean, Mode and Median – Measures of Central Tendency
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A Guide To Complete Statistics For Data Science Beginners!

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