NCERT Example 3 — Statistics

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.

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

\sum f_i=45,\qquad \sum f_iu_i=-106

\bar{x}=200+20\left(\frac{-106}{45}\right)

=200-47.111\ldots=152.888\ldots

Thus these 45 bowlers took about 152.89 wickets on average.

\boxed{\bar{x}\approx152.89\text{ wickets}}