Discussion
The difference between the median and the mode of the observations
13, 16, 12, 14, 19, 12, 13, 14, 12, 15, 16, 15, 18, 19 is :
Answer: B
The difference is 2·5.
Arrange the 14 observations in order:
12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 18, 19, 19
With an even number of values, the median is the mean of the 7th and 8th:
\[ \begin{aligned} \text{Median} &= \frac{14 + 15}{2} = 14.5 \\ \text{Mode} &= 12 \\ 14.5 - 12 &= 2.5 \end{aligned} \]
12 is the mode because it occurs three times, more than any other value. Reading the middle values from the unsorted list instead of the sorted one is the usual error, and it does not give 2·5.
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