Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.33

Analysis Table

Column Sizes of items having maximum frequency

1 65

2 63 64

3 64 65

4 62 63 64

5 63 64 65

6 64 65 66

No. of items 1 3 5 4 1

From the above table, we find 64 is the size of the item which is most frequented. The mode is, therefore,
located at 64.
[Note. At glance from column (1) one might think that 65 is the mode since it contains maximum frequency.
This impression is corrected by the process of grouping. So it is not advisable to locate the mode merely by
inspection.]
(C) For continuous Series.
By inspections or by preparing Grouping Table and Analysis Table, ascertain the modal class. Then to find
the exact value of mode, apply the following formula.

Mode =^10
1 0 2

I f f i.

2f f f

+ − ×

− −

Where, I = lower class-boundary of modal class
f 1 = frequency of modal class.
f 0 = frequency of the class preceding modal class.
f 2 = frequency of the class succeeding the modal class.
i = size of the class- interval of modal class.
Note : the above formula may also be expressed as follows :

Mode = ( ) ( )
1 0 1
1 0 1 2 1 2

l f f i l i.

f f f f

+ − × = + ∆ ×

− + − ∆ + ∆ Where ∆^1 = f^1 – f0-∴^ ∆^2 = f^1 – f2-.

Example 36 : Compute mode of the following distribution.
Marks No. of students
10–20 5
20–30 8
30–40 12
40–50 16
50–60 10
60–70 8