Page 128 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Unit 8: Measurement of Central Tendency

Interpretation of Median Notes

The median represents the central point of data where frequencies are halved. In the above
example there are fifty percent of cases namely 17, having scores above 15, i.e., the median.
Educational Situations and Use of Median

Median is used in the following situations :
• when incomplete distribution is given.
• when the point dividing the distribution into two equal parts is needed.

• when a distribution is markedly skewed. That is, one or more very extreme cases are
there to one side of the distribution. Say, in a group of 20 students 18 of them are scoring
very low marks say 15 to 40 out of 100 and two students score 95 and 100. Such distributions
are known as skewed.

• when interest is limited to finding the placement of cases in the lower half or upper half
of the distribution and not in finding how far they are from the central point.

Limitations of Median
Median is not dependent on all the observations and ignores their numerical values. It cannot
be used as the centre of gravity of the distribution. Also, it cannot be used for inferential
statistical analyses.

8.4 Data on Equal Interval Scale and Measure of Central Tendency —
The Mean

Mean is calculated when the data are complete and presented on equal interval scale. It is
most popularly known as the ‘Arithmetic Mean’. Mean provides an accurate description of the
sample and indirectly, that of the population. It is the sum of measurements divided by their
number.

Mean = “X/N
Where, “X = Sum of all values, N = Number of cases

Did u know? Mean of a distribution of scores may be defined as the point on the scale
of measurement obtained by dividing the sum of all the scores by the
number of scores.

Calculating Mean for Ungrouped Data
When raw data are given the Mean is computed by adding all these values and dividing by
the total number.
Example

Compute Mean for the scores given below :
25, 36, 18, 29, 30, 41, 49, 26, 16, 27
Mean ZX = 25 + 36 + 18 + 29 + 30 + 41 + 49 + 26 + 16 + 27

= 297/10 = 29.7

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