Page 114 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 6: Measures of Central Tendency

6.5.1 Determination of Mode Notes

When data are either in the form of individual observations or in the form of
ungrouped frequency distribution

Given individual observations, these are first transformed into an ungrouped frequency
distribution. The mode of an ungrouped frequency distribution can be determined in two ways,
as given below:
1. By inspection or

2. By method of Grouping
1. By inspection: When a frequency distribution is fairly regular, then mode is often
determined by inspection. It is that value of the variate for which frequency is maximum.
By a fairly regular frequency distribution we mean that as the values of the variable
increase the corresponding frequencies of these values first increase in a gradual manner
and reach a peak at certain value and, finally, start declining gradually in, approximately,
the same manner as in case of increase.

Example: Compute mode of the following data:
3, 4, 5, 10, 15, 3, 6, 7, 9, 12, 10, 16, 18,

20, 10, 9, 8, 19, 11, 14, 10, 13, 17, 9, 11
Solution.
Writing this in the form of a frequency distribution, we get
Values : 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Frequency: 2 1 1 1 1 1 3 4 2 1 1 1 1 1 1 1 1 1
Mode = 10
Remarks:

1. If the frequency of each possible value of the variable is same, there is no mode.
2. If there are two values having maximum frequency, the distribution is said to be bi-
modal.

Example: Determine the mode of the following distribution
X : 10 11 12 13 14 15 16 17 18 19
f : 8 15 20 100 98 95 90 75 50 30

Solution:
This distribution is not regular because there is sudden increase in frequency from 20 to 100.
Therefore, mode cannot be located by inspection and hence the method of grouping is used.
Various steps involved in this method are as follows:
1. Prepare a table consisting of 6 columns in addition to a column for various values of X.

2. In the first column, write the frequencies against various values of X as given in the
question.
3. In second column, the sum of frequencies, starting from the top and grouped in twos, are
written.

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