Page 113 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes Making a cumulative frequency table we have
. .
0 5 15 15
5 10 125 140
10 15 140
15 20 66 206
20 25 90 296
25 30 4 300
N 300
Here = =150 . Since median is given as 11, the median class is 10 - 15.
2 2
150 140
Hence, 11 10 5 or x = 50.
x
Also, frequency of the age group 20-25 is 90 – 50 = 40.
Self Assessment

State whether the following statements are true or false:
16. The values of a variable that divide a distribution into four equal parts are called quartiles.
17. Q , Q and Q , known as the first, second and the third quartile respectively.
1 2 3
18. Deciles divide a distribution into 10 equal parts.

19. There are, in all, 9 deciles denoted as D , D , ...... D respectively.
1 2 9
20. Percentiles divide a distribution into 100 equal parts.
21. There are, in all, 99 percentiles denoted as P , P , ...... P , ...... P , ...... P , ...... P respectively.
1 2 25 40 60 99
6.5 Mode

Mode is that value of the variate which occurs maximum number of times in a distribution and
around which other items are densely distributed. In the words of Croxton and Cowden, “The
mode of a distribution is the value at the point around which the items tend to be most heavily
concentrated. It may be regarded the most typical of a series of values.” Further, according to
A.M. Tuttle, “Mode is the value which has the greatest frequency density in its immediate
neighbourhood.”
If the frequency distribution is regular, then mode is determined by the value corresponding to
maximum frequency. There may be a situation where concentration of observations around a
value having maximum frequency is less than the concentration of observations around some
other value. In such a situation, mode cannot be determined by the use of maximum frequency
criterion. Further, there may be concentration of observations around more than one value of
the variable and, accordingly, the distribution is said to be bi-model or multi-model depending
upon whether it is around two or more than two values.
The concept of mode, as a measure of central tendency, is preferable to mean and median when
it is desired to know the most typical value, e.g., the most common size of shoes, the most
common size of a ready-made garment, the most common size of income, the most common
size of pocket expenditure of a college student, the most common size of a family in a locality,
the most common duration of cure of viral-fever, the most popular candidate in an election, etc.

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