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Quantitative Techniques – I

Notes Demerits
1. It is not based on all the observations.
2. It is not capable of further mathematical treatment.
3. In certain cases mode is not rigidly defined and hence, the important requisite of a good
measure of central tendency is not satisfied.
4. It is much affected by the fluctuations of sampling.
5. It is not easy to calculate unless the number of observations is sufficiently large and reveal
a marked tendency of concentration around a particular value.
6. It is not suitable when different items of the data are of unequal importance.
7. It is an unstable average because, mode of a distribution, depends upon the choice of
width of class intervals.

6.5.3 Relation between Mean, Median and Mode

The relationship between the above measures of central tendency will be interpreted in terms of
a continuous frequency curve.
If the number of observations of a frequency distribution are increased gradually, then
accordingly, we need to have more number of classes, for approximately the same range of
values of the variable, and simultaneously, the width of the corresponding classes would
decrease. Consequently, the histogram of the frequency distribution will get transformed into
a smooth frequency curve, as shown in Figure 6.2.
Figure 6.2: Frequency Curve

For a given distribution, the mean is the value of the variable which is the point of balance or
centre of gravity of the distribution. The median is the value such that half of the observations
are below it and remaining half are above it. In terms of the frequency curve, the total area under
the curve is divided into two equal parts by the ordinate at median. Mode of a distribution is a
value around which there is maximum concentration of observations and is given by the point
at which peak of the curve occurs.
For a symmetrical distribution, all the three measures of central tendency are equal i.e. = M =
d
M , as shown in Figure 6.3.
o
Figure 6.3: Symmetrical Distribution

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