Page 132 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Unit 8: Measurement of Central Tendency

upon the nature of the distribution. In a perfectly symmetrical unimodal distribution these Notes
three measures come very close to each other or even become identical. As the symmetry of
the distribution varies the three measures (Mean, Median and Mode) register divergence. A
very crude sort of relationship among them is shown by the equation :
Mode = 3 Median – 2 Mean

8.5 Comparison of Mean, Median and Mode

The Characteristics of Mean, Median and Mode have been discussed in the preceding sections
besides mentioning some situations where they can be appropriately used. Mean, Median and
Mode differ from each other on various counts. These should be used as per the nature of the
data indicated, by the scale of measurement used and the purpose in hand. However, the
mean is a more precise, reliable and stable measure. Its use should be avoided when data are
skewed or truncated. If some decision is to be taken on the face value of data, mode is the best
measure. But to have a suitable measure when data are incomplete or skewed, Median may
be preferred. If further statistical analysis is to be carried out we should go for Mean. It will
not be desirable to consider any one of them to be superior or inferior in all situations as it
is rather contextual. We should consult an expert if required.

Task Make a chart on the comparison of mean, median and mode.

8.6 Selection of an Appropriate Average

Selection of an appropriate average requires experience and insight to examine the nature of
data and the purpose in hand. A careful study of the various sections of this chapter namely
13.4.3, 13.4.4, 13.5.5, 13.5.6, 13.6.4, 13.6.5,13.6.7 and 13.7 wouldguide you in taking suitable
decisions. The Scale of measurement on which data are available also plays an important role
for selecting an appropriate average. It is also possible to convert data from one to the other
scale of measurement. The purpose of using the average should be kept. in view while selecting
a measure of central tendency.

8.7 Summary

• Measurement is the means of providing quantitative description where numbers are
assigned to objects or events according to some rules.
• 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.
• Mode has the limitations associated with the scale of measurement for which it stands.

• The median represents the central point of data where frequencies are halved.

8.8 Keywords

Central Tendency : Such descriptions of group performances are known as measures of
central tendency.
Arithmetic Mean : Mean is calculated when the data are complete and presented on equal
interval scale. It is most popularly known as the ‘Arithmetic Mean’.

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