Page 70 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Since the value 64 has been repeated the maximum number of times, i.e., 5, the modal weight is 64 kg.
It should be noted that by inspection one is likely to say that the modal value is 65 since it has the
highest frequency, i.e., 24. But this is incorrect as revealed by the analysis table and grouping table.
Calculation of Mode — Continuous Series

Steps:

(i) By preparing grouping table and analysis table or by inspection ascertain the modal class.
(ii) Determine the value of mode by applying the following formula:
Δ
M 0 = L+ 1 i × ... (i)
Δ+ Δ 2
1
where L = Lower limit of the modal class; Δ = the difference between the frequency of the
1
modal class the frequency of the pre-modal class, i.e., preceding class (ignoring signs); Δ = the
2
difference between the frequency of the modal class and the frequency of the post-modal class,
i.e., succeeding class (ignoring signs); i = the size of the class-interval of the modal class.
Another form of this formula is:

f – f
M 0 = L+ 1 0 i × ... (ii)
2 f 1 – f 0 – f 2
where L = Lower limit of the modal class; 1 = frequency of the modal class, 0 = frequency of
f
f
f
the class preceding the modal class; 2 = frequency of the class succeeding the modal class.
While applying the above formula for calculating mode it is necessary to see that the class
intervals are uniform throughout. It they are unequal they should first be made equal on the
assumption that the frequencies are equally distributed throughout the class, otherwise we
will get misleading results.

In the latter case the value of mode cannot be determined by the above formula and
hence mode is ill-defined.

A distribution having only one mode is called unimodal. If it contains more than one mode, it is
called bimodal or multimodal. If collected data produce a bimodal distribution, the data themselves
should be questioned. Quite often such a condition is caused when the size of the sample is
small; the difficulty can be remedied by increasing the sample size. Another common cause is
the use of non-homogeneous data. Instances where a distribution is bimodal and nothing can
be done to change it, the mode should not be used as a measure of central tendency.
Where mode is ill-defined, its value may be ascertained by the following formula based upon
the relationship between mean, median and mode.
Mode = 3 Median – 2 Mean ... (iii)

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