After reading this article you will learn about: 1. Meaning of Median 2. Merits of Median 3. Demerits of Median.
Meaning of Median:
Median is the value of the middle item of a series when arranged in order of magnitude (ascending or descending order).
M = size of (n+ 1)/2 th item,
where M stands for median and n for the number of items.
For example,
For example,
Median from grouped data can be calculated from the following formula:
Where l1 = lower limit of median class,
N = total frequency,
F = cumulative frequency,
fm = frequency of the median class and
i = class interval of median class.
For example, find out median value from the following distribution:
Merits of Median:
i. Easily calculated and better understood and not affected by the values of the extreme items.
ii. It can be located merely by inspection in many cases.
iii. It gives best result in a study of those phenomena which are incapable of direct quantitative measurement, for example, assessment of madness among mentally retarded patients. In such case it is possible to arrange a group of patients in ascending or descending order in relation to the degree of madness and thus to locate a person whose madness can be said to be average.
Demerits of Median:
i. Median may not be representative of a series in many cases.
ii. It is not suitable for further algebraic treatment.
iii. When median has to be calculated in continuous series it requires interpolation.
iv. Median ignores the values of extremes in the series.
v. Median is likely to be affected by the fluctuations of sampling.
Example 1:
Find out mean, mode and median from the following data and draw the frequency distribution curve:
Solution:
Frequency Distribution Curve:
Such type of distribution is normal distribution, symmetrically distributed items on both sides of the peak. The curve is normal distribution curve.
The normal distribution curve has the following properties:
i. Mean, mode and median coincides.
ii. Single peak with symmetric distribution of the variables on either side.
iii. The normal distribution curve has a fixed mathematical characteristic feature independent of the scale, magnitude and unit of mean and standard error.