Page 125 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Methodology of Research and Statistical Techniques

Notes
Example

Find the Median for the set of scores given below :
12, 17, 18, 15, 20, 19
The first step towards finding the Median would be to arrange the given scores serially (ascending
or descending order). You will get 12, 15, 17, 18, 19, 20. Of the six scores here two scores are
below 17 and two above 18. The scores 17 and 18 fall in the middle of the distribution. Here
we are not in a position to define median unless we divide this interval covering both the
middle scores (17 and 18) into two equal halves. The mid point of the interval 16.5 (lower limit
of 17) to 18.5 (upper limit of 18) would be 17.5. Hence 17.5 is the point which divides the
distribution into two equal halves. Since there lie exactly 50 percent cases below and above the
point, 17.5 it is the Median of the given distribution.
Conclusion : From the above two examples it may be concluded that the median can be
th
obtained by finding out the (n+1) /2 term when scores have been arranged in ascending or
descending order. If, you examine previous example, there were 7 cases (odd number). The
th
(n+1) /2 term will be 7+1/2 = 4th term, which happens to be 9. In this example, there were
th
th
6 cases (even number) where (n+1) term comes to be (6+1)/2 = 3.5 term. Thus Median is
found by averaging the third and fourth term i.e., (17+18)/2 = 17.5.
After calculating the median, you may like to go back and check that half the values do fall
below and above the value you have identified as median. This will help you to avoid making
errors.

Example

Find the median for the given set of scores :
16, 28, 32, 45, 75, 28, 26, 34, 37, 52, 18
We first arrange the scores in ascending order (we could arrange these in descending orders
as well) :
16, 18, 26, 28, 28, 32, 34, 37, 45, 52, 75
There are eleven scores in all. The (n+1)/2th term i.e., (11+1)/2 = 6th term will be the median.
Median = 32.
Calculation of Median in Grouped Data
As stated earlier, Median is a point on the scale of measurement below which lie exactly fifty
percent cases. Obviously fifty percent cases will be above it. For calculating the median, the
assumption made in case of grouped data is that frequencies are evenly distributed within the
class interval.
Let us take an example to illustrate the point.
Example

Find the Median for the distribution given below :
Class Interval Frequency
45–49 3 13 = number of cases above the

40–44 4 interval containing Median
35–39 6 8 = cases in the Median class (fm)

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