(Q8). The below distribution shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify ?

Number of wickets	20-60	60-100	100-150	150-250	250-350	350-450
Number of bowlers	7	5	16	12	2	3

Solution : Here, the class size varies, and the x_i's are large. Let us still apply the step deviation method with a = 200 and h = 20. Then, we obtain the data as given in the table.

Number of Wickets	Number of bowlers (fi)	xi	di = xi - a	ui = xi - a h (h = 20)	fiui
20-60	7	40	-	-	-
60-100	5	80	-	-	-
100-150	16	125	-	-.75	-
150-250	12	200(a)
250-350	2	300
350-450	3	400
Total	45	-	-	-	-

So, x̄ = a + [

∑f_iu_i

∑f_i

] × h = 200 +

-

45

× 20 = .89