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.

# 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.

1. A
150 or 151
2. B
152 or 153
3. C
153 or 154
4. D
154 or 155

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### Solution:

The following data is given:
As we know that the mean is the average of the given data set.
For grouped data and by direct method it is computed using,
.
To find the mean number of wickets, make a table describing the information given and find $\sum _{}^{}{f}_{i}$ and $\sum _{}^{}{f}_{i}{x}_{i}$.
Substitute $\sum _{}^{}{f}_{i}=45$ and $\sum _{}^{}{f}_{i}{x}_{i}=-53$ into the formula,
$\mathit{Mean}=a+\left(\frac{\sum _{}^{}{f}_{i}{x}_{i}}{\sum _{}^{}{f}_{i}}\right)×h$

$⇒\mathit{Mean}=200-47.11$
$⇒\mathit{Mean}=152.89$
Therefore, the mean number of wickets is 152 or 153.
Hence, option 2 is correct.

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