The distribution 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.
$\begin{matrix} No. of wickets & 20 - 50 & 50 - 100 & 100 - 150 & 150 - 250 & 250 - 350 & 350 - 450 No. of bowlers & 7 & 5 & 16 & 12 & 2 & 4 \end{matrix}$

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Solution

Since, the class intervals are not continuous, we will use Direct Method to find the mean.
$\begin{matrix} No. of wickets & 20 - 50 & 50 - 100 & 100 - 150 & 150 - 250 & 250 - 350 & 350 - 450 No. of bowlers (f_{i}) & 7 & 5 & 16 & 12 & 2 & 4 Class Marks (x_{i}) & 35 & 75 & 125 & 175 & 300 & 400 x_{i} f_{i} & 245 & 375 & 2000 & 2100 & 600 & 1600 \end{matrix}$
$∴ \sum f_{i} = 46$ and $\sum f_{i} x_{i} = 6920$
Hence, Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{6920}{46} = 150.43$

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The distribution 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 wickets20−5050−100100−150150−250250−350350−450No. of bowlers75161224