Measures of Central Tendency, Meaning and Objectives

Measures of central tendency are fundamental concepts in statistics. They provide valuable insights into the typical or central values within a dataset. As a statistical measure, central tendency summarises data distribution by identifying a representative value that best represents the entire set.

What Is the Measures of Central Tendency?

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Mean (Arithmetic Mean)?

• Arithmetic Mean
• Geometric Mean
• Harmonic Mean

Mean = (Sum of all the observations/Total number of observations)

Median

Ungrouped Data

Odd Number of Values (n=odd): Median=(𝑛+1/2)th observation

Even Number of Values (n=even):Median=(𝑛2)th observation+(𝑛2+1)th observation/2

Grouped Data

Median=𝑙+(𝑛2−𝑐𝑓𝑓)×ℎ

• 𝑙 is the lower limit of the median class,
• 𝑓 is the frequency of the median class,
• ℎ is the width of the median class,
• 𝑐𝑓 is the cumulative frequency of the class preceding the median class.

Mode

• Unimodal : A set with one mode.
• Bimodal : A set with two modes.
• Trimodal : A set with three modes.
• Multimodal : A set with four or more modes.

Mode = L + (f 1– f 0/2f 1– f 0– f 2 )*h.

• l=lower limit of modal class
• fm=frequency of modal class
• f1=frequency of class preceding modal class
• f2=frequency of class succeeding modal class and h=class width.

Distribution of Central Tendency

1. Normal Distribution :

Mean = Median = Mode

1. Skewed Distribution :

• Right Skew:

Mean > Median > Mode

• Left Skew:

Mean < Median < Mode

The objective of Measures of Central Tendency