Discussion

The following observations have been written in the ascending order :

28, 31, 47, 51, a, a + 3, 71, 74, 78, 90

If the median of the data is 61.5, then the mean of the data is :

Answer: B

The mean is 59.3.

There are 10 observations, so the median is the average of the 5th and 6th, which are a and a + 3.

\[ \begin{aligned} \frac{a + (a + 3)}{2} &= 61.5 \\ 2a + 3 &= 123 \\ a &= 60 \end{aligned} \]

So the data are 28, 31, 47, 51, 60, 63, 71, 74, 78, 90, whose sum is 593.

\[ \text{Mean} = \frac{593}{10} = 59.3 \]

Forgetting the + 3 in the sixth value gives a sum of 590 and a mean of 59, which is not offered; none of the other options fits a = 60.

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