Median Frequency Distribution

Introduction to median frequency distribution:
A tabular arrangement of the data showing the frequency with which each successive value of the variable occurs is called a frequency distribution.Frequency distribution is classified into two types’ continuous distribution and discrete distributions. And median is known as if the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. Here, we are going to study about median in frequency distribution.

Median in Types of Frequency Distribution

It has two types, they are

Median in discrete distribution, and
Median in continuous distribution.
Median in Discrete Frequency Distribution :

Median in discrete distribution:

In any discrete distribution if all items can be arranged in order of magnitude, preferably the highest score at the top, the middle point of the array gives the position of the median and the score at that point is called the median or the median score. There will be an equal number of items above and below the median.

Ex: If seven boys of different heights are made to stand in a row, the tallest first, the next tallest next, and so on
Solution: The median height is of the fourth boy from either end. If there is an even number of boys, say eight, it would be natural to take as median the height midway among that one of the fourth and that of the fifth boy. It is given by ‘(4 +5)/2’ or 4.5th from either end.
In either case, whether n is odd or even, the position of the median is given by the number ‘(n+1)/2’ and the score at the point is called the median.

Median in Continuous Frequency Distribution

We know that continuous distribution can be represented by a histogram. Moreover, we also know that the total frequency (n) of a continuos distribution is equal to area of the histogram with frequency density.
The median for a continuous distribution is that value of the variable the ordinate at which divides the histogram into two equal parts of the equal area.
Hence the position of the median in the case of a continuous distribution is given by ‘n/2’ (and not ‘(n+1)/2’ ). The unit of the median is the same as that of the variates.

Ex: Consider a group of 17 students with the following heights (in cm): 106, 110, 123, 125, 117, 120, 112, 115, 110, 120, 115, 102, 115, 115,109, 115, 101.

Solution:First arrange the data in ascending or descending order, 101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125

Now the median of the given set of data is the middle number or term, that is 115.

So the median of this continuous distribution is 115.

Mean of this distribution is,

‘(106 + 110+123+125+117+120+112+115+110+120+115+102+115+115+109+115+ 110) /17’