Page 105 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Demerits

Although, arithmetic mean satisfies most of the properties of an ideal average, it has certain
drawbacks and should be used with care. Some demerits of arithmetic mean are:
1. It can neither be determined by inspection nor by graphical location.

2. Arithmetic mean cannot be computed for a qualitative data; like data on intelligence,
honesty, smoking habit, etc.
3. It is too much affected by extreme observations and hence, it does not adequately represent
data consisting of some extreme observations.
4. The value of mean obtained for a data may not be an observation of the data and as such
it is called a fictitious average.
5. Arithmetic mean cannot be computed when class intervals have open ends. To compute
mean, some assumption regarding the width of class intervals is to be made.

6. In the absence of a complete distribution of observations the arithmetic mean may lead to
fallacious conclusions. For example, there may be two entirely different distributions
with same value of arithmetic mean.
7. Simple arithmetic mean gives greater importance to larger values and lesser importance
to smaller values.

Self Assessment

State whether the following statements are true or false:

8. Arithmetic Mean is defined as the sum of squares of observations divided by the number
of observations.
9. In case of simple arithmetic mean, equal importance is not given to all the observations.

10. In weighted arithmetic mean, the importance given to various observations is same.
11. In an individual frequency distribution, we only know the number of observations in a
particular class interval and not their individual magnitudes.

12. The accuracy of arithmetic mean calculated for a grouped frequency distribution does not
depends upon the validity of the fundamental assumption.

6.3 Median

Median of distribution is that value of the variate which divides it into two equal parts. In terms
of frequency curve, the ordinate drawn at median divides the area under the curve into two
equal parts. Median is a positional average because its value depends upon the position of an
item and not on its magnitude.

6.3.1 Determination of Median

When Individual Observations are given

The following steps are involved in the determination of median:
1. The given observations are arranged in either ascending or descending order of magnitude.

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