Discussion

Following data shows the number of wickets taken by a player in last 11 matches played by him/her :

1, 0, 2, 4, 0, 3, 1, 1, 2, 4, 1

What is the difference between the mean and mode of the above data ?

Answer: C

The difference is \(\frac{8}{11}\).

The sum of the 11 values is 1 + 0 + 2 + 4 + 0 + 3 + 1 + 1 + 2 + 4 + 1 = 19, and 1 occurs most often (four times), so the mode is 1.

\[ \begin{aligned} \text{mean} &= \frac{19}{11} \\ \text{mean} - \text{mode} &= \frac{19}{11} - 1 = \frac{8}{11} \end{aligned} \]

Fractions with denominator 9 cannot arise from 11 values, and \(\frac{7}{11}\) would need the wickets to total 18.

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