Page 68 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Since the value 120 occurs the maximum numbers of times, i.e., 4, hence the modal value is 120.

Thus the process of determining mode in case of individual observations essentially
involves grouping of data.

When there are two or more values having the same maximum frequency one cannot say which is
the modal value and hence mode is said to be ill-defined. Such a series is also known as bimodal or
multimodal. For example, observe the following data:
Income (in Rs.) 610, 620, 630, 620, 610, 640, 630, 620, 630, 640.

Size of item No. of times it occurs
610 2
620 3
630 3
640 2

Mode is ill-defined in this case.
Calculation of Mode — Discrete Series

In discrete series quite often mode can be determined just by inspection, i.e., by looking to that value
of the variable around which the items are most heavily concentrated. For example, observe the
following data:

Size of garment No. of persons

28 10
29 20
30 40
31 65
32 50
33 15
From the above data we can clearly say that the modal size is 31 because the value 31 has occurred
the maximum number of times, i.e., 65. However, where the mode is determined just by inspection,
an error of judgment is possible in those cases where the difference between the maximum frequency
and the frequency preceding it or succeeding it is very small and the items are heavily concentrated
on either side. In such cases it is desirable to prepare a grouping table and an analysis table. These
tables help us ascertaining the modal class.
A grouping table has six columns. In column 1 the maximum frequency is marked or put in a circle;
in column 2 frequencies are grouped in two’s, in column 3 leave the first frequency and then group
remaining in two’s; in column 4 group the frequencies in three’s; in column 5 leave the first frequency
and group the remaining in three’s; and in column 6 leave the first two frequencies and then group
the remaining in three’s. In each of these cases take the maximum total and mark it in a circle or by
bold type.

62 LOVELY PROFESSIONAL UNIVERSITY