Question

The distribution given below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method.

No. of Wickets	$20-60$	$60-100$	$100-150$	$150-250$	$250-350$	$350-450$
No. of Bowlers	$7$	$5$	$16$	$12$	$2$	$3$

Answer 1

Number of Wickets	Number of Bowlers $\left(f_i\right)$	Class Mark $\left(x_i\right)$	$f_i{x}_i$
$20-60$	$7$	$\frac{20+60}{2}=40$	$7\times 40=280$
$60-100$	$5$	$\frac{60+100}{2}=80$	$5\times 80=400$
$100-150$	$16$	$\frac{100+150}{2}=125$	$16\times 125=2000$
$150-250$	$12$	$\frac{150+250}{2}=200$	$12\times 200=2400$
$250-350$	$2$	$\frac{250+350}{2}=300$	$2\times 300=600$
$350-450$	$3$	$\frac{350+450}{2}=400$	$3\times 400=1200$
	$\sum f_i=45$		$\sum f_i{x}_i=6880$

This problem can be solved using direct method as class interval is different.

We know tha,

Mean $\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}$

Now, the required mean is,

$\overline{x}=\frac{6880}{45}=152.89$