Interview Prep
Career
GenAI
Prompt Engg
ChatGPT
LLM
Langchain
RAG
AI Agents
Machine Learning
Deep Learning
GenAI Tools
LLMOps
Python
NLP
SQL
AIML Projects

Reading list

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 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
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

Mean, Mode and Median – Measures of Central Tendency

U
Ubaid Last Updated : 04 Jul, 2023
7 min read

In statistics, central tendency measures provide valuable insights into a dataset’s typical or central values. They help us understand the overall distribution and characteristics of a set of observations by identifying the central or representative value around which the data tend to cluster. This article will explore the concept of central tendency measures – mean, median, and mode in detail,

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

Table of contents

What are Data Types?

Data is largely divided into two major categories, quantitative and qualitative. They are further divided into other parts. Refer to the graph given below for reference –

Types of Data

Types of Data

  • Quantitative data: This type of data consists of numerical values that can be measured or counted. Examples include time, speed, temperature, and the number of items.
  • Qualitative data: This type includes non-numerical values representing qualities or attributes. Examples include colors, yes or no responses, and opinions.

Types of Quantitative Data

  • Discrete data: This refers to separate and distinct values, typically counting numbers. For instance, the numbers on a dice or the number of students in a class are discrete data points.
  • Continuous data: This type of data can take on any value within a range and be measured with high precision. Examples include height, weight, and temperature.

Data Types Based on Level of Measurement

Data can be further classified into four types based on the level of measurement: nominal, ordinal, interval, and ratio.

  • Nominal data: This represents categorical information without any inherent order or ranking. Examples include gender, religion, or marital status.
  • Ordinal data: This type has a defined order or ranking among the values. Examples include exam grades (A, B, C) or positions in a competition (1st place, 2nd place, 3rd place).
  • Interval data: Interval data has a defined order and equal intervals between the values. An example is the Celsius temperature scale, where the difference between 30°C and 20°C is the same as the difference between 20°C and 10°C.
  • Ratio data: Ratio data possesses all the characteristics of interval data but has a meaningful zero point. In addition to setting up inequalities, ratios can also be formed with this data type. Examples include height, weight, or income.

What is Measure of Central Tendency?

We should first understand the term Central Tendency. Data tend to accumulate around the average value of the total data under consideration. Measures of central tendency will help us to find the middle, or the average, of a data set. If most of the data is centrally located and there is a very small spread it will form an asymmetric bell curve. In such conditions values of mean, median and mode are equal.

Mean, Median, Mode

Let’s understand the definition and role of mean, median and mode with the help of examples –

Mean

It is the average of values. Consider 3 temperature values 30 oC, 40 oC and 50 oC, then the mean is (30+40+50)/3=40 oC.

Median

It is the centrally located value of the data set sorted in ascending order. Consider 11 (ODD) values 1,2,3,7,8,3,2,5,4,15,16. We first sort the values in ascending order 1,2,2,3,3,4,5,7,8,15,16 then the median is 4 which is located at the 6th number and will have 5 numbers on either side.

Central Tendency data
Central Tendency ascending order

If the data set is having an even number of values then the median can be found by taking the average of the two middle values. Consider 10 (EVEN) values 1,2,3,7,8,3,2,5,4,15. We first sort the values in ascending order 1,2,2,3,3,4,5,7,8,15 then the median is (3+4)/2=3.5 which is the average of the two middle values i.e. the values which are located at the 5th and 6th number in the sequence and will have 4 numbers on either side.

Central Tendency dataset
ascending order

Mode

It is the most frequent value in the data set. We can easily get the mode by counting the frequency of occurrence. Consider a data set with the values 1,5,5,6,8,2,6,6. In this data set, we can observe the following,

Central Tendency frequency table

The value 6 occurs the most hence the mode of the data set is 6.

We often test our data by plotting the distribution curve, if most of the values are centrally located and very few values are off from the center then we say that the data is having a normal distribution. At that time the values of mean, median, and mode are almost equal.

Central Tendency mean media mode

However, when our data is skewed, for example, as with the right-skewed data set below:

right-skewed

We can say that the mean is being dragged in the direction of the skew. In this skewed distribution, mode < median < mean. The more skewed the distribution, the greater the difference between the median and mean, here we consider median for the conclusion. The best example of the right-skewed distribution is salaries of employees, where higher-earners provide a false representation of the typical income if expressed as mean salaries and not the median salaries.

For left-skewed distribution mean < median < mode.  In such a case also, we emphasize the median value of the distribution.

left-skewed

Mean, Median & Mode Example

To understand this let us consider an example. An OTT platform company has conducted a survey in a particular region based on the watch time, language of streaming, and age of the viewer. For our understanding, we have taken a sample of 10 people.

 df=pd.read_csv("viewer.csv")
 df
read
df["Watch Time"].mean()
2.5

df["Watch Time"].mode()
0    1.5
dtype: float64

df["Watch Time"].median()
2.0

If we observe the values then we can conclude the value of Mean Watch Time is 2.5 hours and which appears reasonably correct. For  Age of viewer following results can be obtained,

df["Age"].median()
12.5

df["Age"].mean()
19.9

df["Age"].mode()
0    12
1    15
dtype: int64

The value of mean Age is looked somewhat away from the actual data. Most of the viewers are in the range of 10 to 15 while the value of mean comes 19.9. This is because the outliers present in the data set. We can easily find the outliers using a boxplot.

sns.boxplot(df['Age'], orient='vertical')
boxplot

If we observe the value of Median Age then the result looks correct. The value of mean is very sensitive to outliers.

Now for the most popular language, we can not calculate the mean and median since this is nominal data.

sns.barplot(x="Language",y="Age",data=df)
barplot
sns.barplot(x="Language",y="Watch Time",data=df)
sns.barplot

If we observe the graph then it is seen that the Tamil bar is largest for Language vs Age and Language vs Watch Time graph. But this will mislead the result because there is only one person who watches the shows in Tamil.

df["Language"].value_counts()
Hindi      4
English    3
Tamil      1
Telgu      1
Marathi    1
Name: Language, dtype: int64

df["Language"].mode()
0    Hindi
dtype: object

Result

From the above result, it is concluded that the most popular language is Hindi. This is observed when we find the mode of the data set.

Hence from the above observation, it is concluded that in the sample survey average age of viewers is 12.5 years who watch for 2.5 hours daily a show in the Hindi language.

We can say there is no best central tendency measure method because the result is always based on the types of data. For ordinal, interval, and ratio data (if it is skewed) we can prefer median. For Nominal data, the model is preferred and for interval and ratio data (if it is not skewed) mean is preferred.

Measures of Central Tendency and Dispersion

Dispersion measures indicate how data values are spread out. The range, which is the difference between the highest and lowest values, is a simple measure of dispersion. The standard deviation measures the expected difference between a data value and the mean.

Frequently Asked Questions

Q1. What are the 4 measures of central tendency?

A. The four measures of central tendency are mean, median, mode, and midrange. Central tendency examples include finding the average age in a group, determining the middle value of test scores, or identifying the most frequently occurring color in a survey.

Q2. What is central tendency examples?

A. To find central tendency, calculate the mean by summing all values and dividing by the total number, find the median by locating the middle value, or determine the mode as the most commonly occurring value.

Q3. How do I find central tendency?

A. The best measure of central tendency depends on the type of data and the specific context of the analysis. The mean is commonly used, but other measures may be more appropriate in certain situations.

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

U
Ubaid

Free Courses

Generative AI 4.7

Generative AI - A Way of Life

Explore Generative AI for beginners: create text and images, use top AI tools, learn practical skills, and ethics.
Large Language Models 4.5

Getting Started with Large Language Models

Master Large Language Models (LLMs) with this course, offering clear guidance in NLP and model training made simple.
Prompt Engineering 4.6

Building LLM Applications using Prompt Engineering

This free course guides you on building LLM apps, mastering prompt engineering, and developing chatbots with enterprise data.
LlamaIndex 4.8

Improving Real World RAG Systems: Key Challenges & Practical Solutions

Explore practical solutions, advanced retrieval strategies, and agentic RAG systems to improve context, relevance, and accuracy in AI-driven applications.
RAG systems using LlamaIndex 4.7

Microsoft Excel: Formulas & Functions

Master MS Excel for data analysis with key formulas, functions, and LookUp tools in this comprehensive course.

Recommended Articles

Responses From Readers

Clear

Adnan
Adnan

Informative! Must read article for the beginers in data science. Thank you for simplifying things to understand.

123

Write for us

Write, captivate, and earn accolades and rewards for your work
  • Reach a Global Audience
  • Get Expert Feedback
  • Build Your Brand & Audience
  • Cash In on Your Knowledge
  • Join a Thriving Community
  • Level Up Your Data Science Game
imag

We use cookies essential for this site to function well. Please click to help us improve its usefulness with additional cookies. Learn about our use of cookies in our Privacy Policy & Cookies Policy.

Show details