In this article we will discuss about Median:- 1. Meaning of Median 2. Methods of Determining Median 3. Merits 4. Demerits.
Meaning of Median:
When the values of all items of a series are arranged in increasing (ascending) or decreasing (descending) order it is usually called an array and the middle item of an array is called median. The median divides the series into two groups; one group in which the values of items are less than the middle value and the other group in which the values of the items are greater than the middle item. Median is denoted by Me or Mdn.
The methods of calculating the median are comparatively simple. The value of median is not affected by change in extreme values. If the number of data in a series is odd, the median is the middle value. But if the number of data in a series is even, the median is the average of the two middle values.
Methods of Determining Median:
1. For unclassified and un-tabulated data:
In order to calculate the median, the data are first arranged in increasing or decreasing order and then the following formula is used:
Me = n+1/2, where n = number of items or data.
Example:
The heights (in cm) for 9 plants are given below. Find out the Media Height — 67, 65, 70, 68, 62, 63, 64, 63, 66.
Solution:
The height measurements can be arranged in ascending order as follows:
(ii) For even number of data in the series:
The median is calculated as follows:
Example:
The number of flowers recorded on 10 plants are:
15,10,8,12,13,7,11,14,9,16. Find out the median value of flowers per plant.
Solution:
The given numbers of flowers on 10 plants can be arranged in ascending order as under:
Example:
Calculate the median of the following series of data obtained by measuring the heights of 16 plants: 9, 10, 10, 8, 9, 7, 8, 11,7, 12, 14, 12, 11, 14, 15, 13.
Solution:
The given data of plant heights are arranged in ascending order as follows:
7, 7, 8, 8, 9, 9, 10, 10, 11,11, 12, 12, 13, 13, 14, 14, 15
n = 16 (even number)
2. For Grouped data:
(i) Discontinuous or Discrete series of data. To calculate the median for discrete grouped data, first of all the cumulative frequency of whole series is obtained. The value of data against n+1/2 the cumulative frequency will be the median for odd number of data and the mean of values against n/2+n/2+1th cumulative frequencies will be median for series containing even number of data.
Example:
Calculate the median of the following data obtained by counting the number of flowers on 19 plants.
Example:
Calculate the median for the following data recorded for height (in cm) of 80 plants.
The class values for cumulative frequencies 40 and 41 are included in the class value of cumulative frequency 45 which is 122. Therefore, Median (Me) = 122+122/2 = 122.
(ii) For classified grouped date:
The median is determined in the following way:
(a) First, the cumulative frequency of all the classes are obtained from the given frequencies.
(b) Median class value is determined which is N/2th class.
(c) The n that class is ascertained whose cumulative frequency precedes that of median class (c.f).
(d) The median is calculated by the following formula.
Example:
The number of seeds produced by 55 plants of a plot are given in the following table.
Calculate the median seed number of a plant.
While calculating the median for classified grouped data the following facts must be kept in mind:
(i) Class intervals must be equal for all classes. If not equal, they should be rearranged allowing equal interval as shown below:
(ii) The classes should be presented by exclusive method (for example 10 – 20,20 – 30, 30 – 40 – —and so on).
If the classes are presented in inclusive manner then they should be changed to exclusive one by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit as exemplified below:
Inclusive presentation of classes:
Merits of Median:
1. It is calculated easily and located exactly.
2. It is not affected by abnormally large or small values.
3. Its size cannot be changed much by adding a few more items.
4. Median can be used in quantitative measurements.
Demerits of Median:
1. The median of two or more series cannot be calculated by using the median of the component series.
2. It may not be represented in central data.
3. It cannot be used where weight-age is given to some items.