Paper 4: Fundamentals of Business Mathematics & Statistic

5.34 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Table : Calculation of Mode

Marks No. of students

10–20 5

20–30 8

30–40 12 → f 0

40–50 16 → f 1

50–60 10 → f 2

60–70 8

From the table it is clear that the maximum frequency is 16th : modal class is (40–50)

Here l = 40, f 0 = 12, f 1 = 16, f 2 = 10 (marked in table), i = 10 (= 50 –40)

Mode = 1100 2

l + f - f ×i

2f - f - f

= 40 + 16 -12 ×10

2 ×16 -12 -10

40 4 10

32 22

= + ×

−

40 4 10

10

= + × = 40 + 4 = 44 marks.

Alternatively, D 1 = f 1 –f 0 = 16 –12 = 4,

D 2 = f 1 – f 2 = 16–10 = 6, i = 10, I = 40

Mode =^40 +4 6^4 + ×^10 =^40 + 104 ×^10

= 40 + 4 = 44 marks.

Calculation of Mode From discrete group frequency distribution.

In such cases at first class boundaries are to be formed for applying formula.

Example 37: Compute mode from the following frequency distribution :

Marks No. of students

50–59 5

60–69 20

70–79 40

80–89 50

90–99 30

100–109 6

The class intervals which are in discrete form are first converted into class boundaries.