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Mathematics · Statistics · NCERT Examples

Example 3

A complete, independently verified solution for NCERT Example 3.

Mathematics · Chapter 13 · NCERT Examples

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NCERT Example

Example 3

mean · unequal class intervals · step deviation

The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean and state what it signifies.

Wickets

Bowlers (fᵢ)

20–60

7

60–100

5

100–150

16

150–250

12

250–350

2

350–450

3

Solution

Board-exam working:

The class sizes vary. Use class marks with assumed mean 200 and convenient divisor 20.

Class

fᵢ

xᵢ

dᵢ = xᵢ − 200

uᵢ = dᵢ/20

fᵢuᵢ

20–60

7

40

−160

−8

−56

60–100

5

80

−120

−6

−30

100–150

16

125

−75

−3.75

−60

150–250

12

200

0

0

0

250–350

2

300

100

5

10

350–450

3

400

200

10

30

∑fi=45,∑fiui=−106\sum f_i=45,\qquad \sum f_iu_i=-106
xˉ=200+20(−10645)\bar{x}=200+20\left(\frac{-106}{45}\right)
=200−47.111…=152.888…=200-47.111\ldots=152.888\ldots

Thus these 45 bowlers took about 152.89 wickets on average.

Final answer

xˉ≈152.89 wickets\boxed{\bar{x}\approx152.89\text{ wickets}}