Page 109 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes A perpendicular is dropped from the point of intersection of the two ogives. The point at which
it intersects the X-axis gives median. It is obvious from above figures that median = 2080.

6.3.2 Properties of Median

1. It is a positional average.

2. It can be shown that the sum of absolute deviations is minimum when taken from median.
This property implies that median is centrally located.

6.3.3 Merits, Demerits and Uses of Median

Merits

1. It is easy to understand and easy to calculate, especially in series of individual observations
and ungrouped frequency distributions. In such cases it can even be located by inspection.

2. Median can be determined even when class intervals have open ends or not of equal
width.
3. It is not much affected by extreme observations. It is also independent of range or dispersion
of the data.
4. Median can also be located graphically.
5. It is centrally located measure of average since the sum of absolute deviation is minimum
when taken from median.
6. It is the only suitable average when data are qualitative and it is possible to rank various
items according to qualitative characteristics.
7. Median conveys the idea of a typical observation.

Demerits

1. In case of individual observations, the process of location of median requires their
arrangement in the order of magnitude which may be a cumbersome task, particularly
when the number of observations is very large.
2. It, being a positional average, is not capable of being treated algebraically.
3. In case of individual observations, when the number of observations is even, the median
is estimated by taking mean of the two middle-most observations, which is not an actual
observation of the given data.
4. It is not based on the magnitudes of all the observations. There may be a situation where
different sets of observations give same value of median. For example, the following two
different sets of observations, have median equal to 30.
Set I : 10, 20, 30, 40, 50 and Set II : 15, 25, 30, 60, 90.

5. In comparison to arithmetic mean, it is much affected by the fluctuations of sampling.
6. The formula for the computation of median, in case of grouped frequency distribution, is
based on the assumption that the observations in the median class are uniformly
distributed. This assumption is rarely met in practice.
7. Since it is not possible to define weighted median like weighted arithmetic mean, this
average is not suitable when different items are of unequal importance.

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