Assumptions regarding the size of the class interval

assumptions regarding the size of the class interval of the open-ended
classes. In an extremely asymmetrical distribution, it is not a good measure of
central tendency .
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RESEARCH METHODOLOGY

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2. Median
The median can be computed for ratio, interval or ordinal scale data. The
median is that value in the distribution such that 5 0 per cent of the
observations are below it and 50 per cent are above it. The median for the
ungrouped data is defined as the middle value when the data is arranged in
ascending or descending order of magnitude. In case the number of items in
th
the sample is odd, the value of ( n + 1)/2 item gives the median. However if
there are even number of items in the sample , say of size 2 n , the arithmetic
th th
mean of n and ( n + 1) items gives the median. It is again emphasized that data
needs to be arranged in ascending or descending orders of magnitude before
computing the median.
Given below are a few examples to illustrate the computation of median:
Example 9.2: The marks of 21 students in economics are given 62, 38, 42,
43, 57, 72, 68, 60, 72, 70, 65, 47, 49, 39, 66, 73, 81, 55, 57, 57 and 59. Compute
the median of the distribution.
Solution:
By arranging the data in ascending order of magnitude, we obtain: 38, 39,
42, 43, 47, 49, 55, 57, 57, 57, 59, 60, 62, 65, 66, 68, 70, 72, 72, 73 and 81.
th
The median will be the value of the 11 observation arranged as above.
Therefore , the value of median equals 59 . This means 5 0 per cent of students
score marks below 59 and 50 per cent score above 59.
The median could also be computed for the grouped data. In that case, first of
all, median class is located and then median is computed using interpolation
by using the assumption that all items are evenly spread over the entire class
interval. The median for the grouped data is computed using the following
formula:
Where,
l = Lower limit of the median class
f = Frequency of the median class
CF = Cumulating frequency for the class immediately below the class
containing the median
h= size of the interval of the median class.
Given below is an example to illustrate the computation
of median in the case of grouped data:
Example 9.3: The distribution of dividend declared by seventy-seven
companies is given in the following table . Compute the median of the
distribution.
RESEARCH METHODOLOGY

Solution:
Where,
l = Lower limit of the median class = 30
f = Frequency of the median class = 18
CF = Cumulating frequency for the class immediately below the class
containing the median = 37
h= Size of the interval of the median class =10
Substituting these values in the formula for median, we get
Median = 30.83
The results show that half of the companies have declared less than
30.83 per cent dividend and the other half have declared more than 30.83 per
cent dividend.
The limitation of median as a measure of central tendency is that it does not
use each and every observation in its computation since it is a positional
average.