Discussion
What is the mean of the mode, median and range of the data given below ?
17, 8, 11, 13, 9, 14, 10, 11, 16, 23, 15, 7
Answer: A
The mean of the three measures is 13.
In order the data are 7, 8, 9, 10, 11, 11, 13, 14, 15, 16, 17, 23 (12 values).
\[ \begin{aligned} \text{Mode} &= 11 \\ \text{Median} &= \frac{11 + 13}{2} = 12 \\ \text{Range} &= 23 - 7 = 16 \\ \text{Mean} &= \frac{11 + 12 + 16}{3} = 13 \end{aligned} \]
12 is the median itself, not the mean of the three measures. 12.5 and 13.5 do not arise from the correct mode, median and range; the usual slips are forgetting to sort the data or to average the two middle values for the median.
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