Measures of Central Tendency

Measures of Central Tendency 

Introduction  

• Measures of central tendency are statistical metrics that describe the center or typical value of a dataset. 

• They provide a single value that summarizes the entire dataset by identifying the central position within it. 

• The three main measures of central tendency are: 

• Mean 

• Median 

• Mode 

• Each offers different insights based on the nature and distribution of the data. 

Mean 

• The mean, commonly known as the average, is calculated by summing all the values in a dataset and dividing by the number of values. 

• Formula: 

x−=x1+x2+⋯+xnn𝒙-=𝒙𝟏+𝒙𝟐+⋯+𝒙𝒏𝒏

 

where x1,x2,…,xn are the data values and n is the total number of values.where x1,x2,…,xn are the data values and n is the total number of values.

 

• Best Used When: 

• The data is symmetrical and does not contain outliers, as outliers can significantly affect the mean. 

Median 

• The median is the middle value when the data is arranged in ascending or descending order. 

• If the number of observations is: 

• Odd: The median is the middle number. 

• Even: The median is the average of the two middle numbers. 

• Best Used When: 

• The data is skewed or contains outliers, as the median is less affected by extreme values. 

Mode 

• The mode is the value that appears most frequently in a dataset. 

• A dataset can have: 

• One mode (unimodal) 

• Two modes (bimodal) 

• More than two modes (multimodal) 

• No mode if all values occur only once 

• Best Used When: 

• Analyzing categorical data or identifying the most common value. 

Choosing the Appropriate Measure 

Data Condition	Best Measure	Reason
Symmetric distribution	Mean	Accurately reflects the center when data is balanced
Skewed distribution / Outliers	Median	Less affected by extreme values
Categorical or repeated data	Mode	Identifies the most frequent or popular item

Relation Between Mean, Median, and Mode 

• In biostatistics, these measures help describe different aspects of data distribution: 

• Mean: Average of all data points 

• Median: Middle value when data is ordered 

• Mode: Most frequently occurring value 

• An empirical relation often used: 

Mode≈3×Median−2×MeanMode≈𝟑×Median−𝟐×Mean

 

 

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