Page 110 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 6: Measures of Central Tendency

Uses Notes

1. It is an appropriate measure of central tendency when the characteristics are not measurable
but different items are capable of being ranked.
2. Median is used to convey the idea of a typical observation of the given data.

3. Median is the most suitable measure of central tendency when the frequency distribution
is skewed. For example, income distribution of the people is generally positively skewed
and median is the most suitable measure of average in this case.
4. Median is often computed when quick estimates of average are desired.
5. When the given data has class intervals with open ends, median is preferred as a measure
of central tendency since it is not possible to calculate mean in this case.
Self Assessment

Multiple Choice Questions:
13. ................................. of distribution is that value of the variate which divides it into two
equal parts.
(a) Mean (b) Median
(c) Mode (d) Standard deviation
14. Median is a ................................. average because its value depends upon the position of an
item and not on its magnitude.
(a) Positional (b) Arithmetic
(c) Mathematical (d) Commercial
15. Median is often computed when .................................... of average are desired

(a) Estimate (b) Slow estimate
(c) Quick estimate (d) Negligible estimate

6.4 Other Partition or Positional Measures

Median of a distribution divides it into two equal parts. It is also possible to divide it into more
than two equal parts. The values that divide a distribution into more than two equal parts are
commonly known as partition values or fractiles. Some important partition values are discussed
in the following sections.

6.4.1 Quartiles

The values of a variable that divide a distribution into four equal parts are called quartiles. Since
three values are needed to divide a distribution into four parts, there are three quartiles, viz. Q ,
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Q and Q , known as the first, second and the third quartile respectively.
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For a discrete distribution, the first quartile (Q ) is defined as that value of the variate such that
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at least 25% of the observations are less than or equal to it and at least 75% of the observations
are greater than or equal to it.
For a continuous or grouped frequency distribution, Q is that value of the variate such that the
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area under the histogram to the left of the ordinate at Q is 25% and the area to its right is 75%.
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