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:
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.