Page 124 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Unit 8: Measurement of Central Tendency

Sometimes we may come across bimodal distributions (having two modes) and we do not Notes
easily find one composite measure. Yau may examine the following two situations and appreciate
the limitations of mode :
Situation I : The scores of students in History for Class VII A are as follows :
22, 37, 45, 66, 32, 64, 65, 67, 66, 67, 65, 67, 38, 66, 66, 65, 32, 66, 67, 65, 64, 64, 67, 52, 47, 67,
68, 67, 70
Situation II : The scores of students in Maths for Class IX A are as follows :
18, 20, 23, 24, 24, 25, 24, 24, 24, 30, 35, 40, 46, 48, 50, 56, 62, 62, 62, 62, 60, 47, 38, 62, 62, 24,
28, 62, 80
An inspection of situation I gives the mode of 67 while the adjacent scorer of 64, 65 and 66
seem to be equally potent to become mode. In situation II you notice a bimodal distribution
having two modes at 24 and 62 as both seem to be equally frequent in their own places. We
may thus conclude that mode is only a crude measure which can be of value when a quick
and rough estimate of central tendency is required.

Self Assessment

Fill in the blanks:
1. Data obtained on the nominal scale is of classificatory type and mostly ................... .
2. We frequently deal with ................... in measurement in education.
3. The ................... is the mid point of the class interval having the greatest frequency.

4. Mode can abviously not be subjected to further ................... .

8.3 Data on Ordinal Scale and the Measure of Central Tendency—The
Median

When data have been arranged in rank order the measure of central tendency may be found
by locating a point that divides the whole distribution into two equal halves. Thus median
may be defined as the point on the scale of measurement below and above which lie exactly
50 percent of the cases. Median can therefore be found for truncated (incomplete) data provided
we know the total number of cases and their possible placements on the scale. It may be noted
that median is defined as a point and not as a score or any particular measurement.
Median in Ungrouped Data
For finding out median in ungrouped data let us study the following examples :

Example

Find the Median for the scores :
2, 5, 9, 8, 17, 12, 14
Here we have seven scores. On arranging them in ascending (or descending) order we may
have the sequence of scores as under :
2, 5, 8, 9, 12, 14, 17
We find that there are 3 cases above and below 9 and 9 itself is the mid-point of unit interval
8.5 to 9.5. Thus 9 divides the whole distribution into two equal halves. Therefore 9 would be
the Median in this case.

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