Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.35

Table : Calculation of mode

Class boundaries Frequency

49.5–59.5 5

59.5–69.5 20

69.5–79.5 40

79.5–89.5 50

89.5–99.5 30

99.5–109.5 6

Now modal class is (79.5 – 89.5), since this class has the highest frequency.
Here l = 79.5, f 0 = 40, f 1 = 50, f 2 = 30, i = 10

Mode = 11 00 2
l + f - f ×i
2f - f - f^
79.5 50 40 10
100 40 30
= + − ×
− −

79.5^1010

30

= + × 79.5^10

3

= + = 79.5 + 3.33 = ` 82.83.

Calculation of mode from cumulative frequency distribution :
Example 38 : From the following cumulative frequency distribution of marks of 22 students in Accountancy,
calculate mode :
Marks below 20 below 40 below 60 below 80 below 100
No. of students 3 8 17 20 22
Solution :
At first we are to transfer the above cumulative frequency distribution into a equal group frequency distribution
and hence to calculate mode.

Table : Calculation of mode

Marks students(f)

0–20 3

20–40 5 (= 8 –3)

40–60 9(=17-–8)

60–80 3 (=20–17)

80–100 2 (=22–20)

Modal class is (40–60), as this class has highest frequency.

Here l = 40, f 0 = 5, f 1 = 9, f 2 = 3, i = 20

Mode^10
1 0 2

l + f - f ×i

2f - f - f =

40 9 5 20

2 9 5 3

+ − ×

× − −^

40 4 20

= + 10 × = 40 + 8 = 48 marks.