Discussion
What is the mean of the range, mode and median of the data given below ?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
Answer: B
The mean of the range, mode and median is 9.
Arrange the 15 values in order: 2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19.
\[ \begin{aligned} \text{range} &= 19 - 2 = 17 \\ \text{mode} &= 4 \\ \text{median} &= \text{8th value} = 6 \\ \text{mean} &= \frac{17 + 4 + 6}{3} = 9 \end{aligned} \]
4 is the mode because it occurs three times, more than any other value. Taking the median from the unsorted list (its 8th value is 3) gives \(\frac{17 + 4 + 3}{3} = 8\), a trap option.
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