Discussion
The mean of the median and mode of the observations 30, 61, 55, 56, 60, 20, 26, 45, 28 and 56 is
Answer: B
The mean of the median and mode is 53.
Arrange the ten observations in order: 20, 26, 28, 30, 45, 55, 56, 56, 60, 61.
\[ \begin{aligned} \text{median} &= \frac{45 + 55}{2} = 50 \\ \text{mode} &= 56 \\ \text{mean of the two} &= \frac{50 + 56}{2} = 53 \end{aligned} \]
With an even number of values the median is the average of the 5th and 6th values. Taking 55 alone as the median gives 55.5, and the mode alone is 56, which is why 55 and 56 are traps.
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