Discussion
Arithmetic mean of 12 observations is 40. The smallest and the largest observations are 20 and 60 respectively. If we ignore the smallest and the largest observations then the arithmetic mean of the remaining observations ....................... .
Answer: C
The mean will not change.
\[ \begin{aligned} \text{total} &= 12 \times 40 = 480 \\ \text{removed} &= 20 + 60 = 80 \\ \text{new mean} &= \frac{480 - 80}{10} = 40 \end{aligned} \]
The two values removed average exactly 40, the same as the overall mean, so taking them out leaves the mean unchanged. The data are sufficient, because only the total is needed, not each observation.
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