Measure of Central Tendency

Measure of Central Tendency

Measures of central tendency are statistical measures used to describe the center or typical value of a data set. The three most common measures of central tendency are:

Mean: Mean also known as Average. It is calculated by sum of all observation divided by number of observation.

Individual Series:

Mean = Sum of all observation/Number of observation

Discrete Series:

Mean = Σfx/N where Σf = N

Continuous Series:

x is mid point in continuous series.

Mean = Σfx/N where Σf = N


Median: Median of the distribution is the value of the variable which divides it into two equal parts. The median is thus a positional average.

Individual Series:

First arrange series in ascending order.

—Series of odd number of observation

median is (n/2)th term.

— Series of even number of observation

median is [(n/2)th term+ (n/2 + 1)th term]/2


Discrete Series:

First find cumulative frequencies. The steps for calculating median are as below:

  1. Find N/2, where Σf = N
  2. See the (less than) cumulative frequency (c.f.) just greater than N/2.
  3. the corresponding value of x is median

Continuous Series:

Median = l + h/f (N/2 - c)

where, l is lower limit of median class, h is height of the median class, f is median frequency of the class, c is cumulative frequency of median class.


Mode: Mode is value which occurs most frequently.

Individual Series:

The value which occurs repeatedly in the distribution

Discrete Series:

Mode is value of x corresponding to maximum frequency.

Continuous Series:

Median = l + h(f1-f0)/2f1-f0-f2

where, l is lower limit, h is height, f1 is frequency of modal class, and f0 and f2 are frequencies of the classes preceding and succeeding the modal class respectively.



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