Median:

Median is one of the 5 measures of central tendency that are in general use.

What is a median?

Median of a set of observations is defined as the value of the variable that divides it into two equal parts. In other words, it is the value such that the number of observations above it is equal to the number of observations below it. It is also known as a positional average.

Median for an ungrouped data:

In case of an ungrouped data, the values have to be arranged first in ascending or descending order. If the number of observations is odd, then the median is the middle/central value. If the number of observations is even, then there exists 2 middle terms and the median can be evaluated by taking the arithmetic mean of them.

Median for a discrete frequency distribution:

In case of discrete frequency distribution, median is determined by considering the cumulative frequencies. The steps involved are as follows:

• Find N/2, where N = ∑ fi , i=1 to n
• Look at the (less than) cumulative frequency just greater than N/2.
• The corresponding value of x is median.

Median for a continuous frequency distribution: In case of continuous frequency distribution, the class tallying to the cumulative frequency just above N/2 is called the median class and the median value is got by the following formula:

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

Where l = lower limit of the median class

h = magnitude of the median class

f = frequency of the median class

c = cumulative frequency of the class preceeding the median class

N = ∑ f

The above formula can be used only for continuous classes without any gaps. In case of continuous classes with gaps, the classes have to be converted to continuous classes without gaps. This would affect the value of the lower limit of the median class.

Merits of Median:

The merits of median are as follows:

• Median is strictly defined.
• Median is easily understood and easily evaluated. In some cases, it can be identified simply through inspection.
• Median does not get affected by extreme values.
• Median can be estimated for distributions with open - end classes.