Discussion
The mean of observations (arranged in ascending order) 42, 48, x + 15, x + 17, x + 20, 58 and 60 is 53. The median of the data is
Answer: B
The median is 54.
Use the mean to find x. Seven observations with mean 53 have a total of 7 × 53 = 371:
\[ \begin{aligned} 42 + 48 + 3x + 52 + 58 + 60 &= 371 \\ 260 + 3x &= 371,\ x = 37 \end{aligned} \]
The data are 42, 48, 52, 54, 57, 58, 60. With seven values in ascending order, the median is the fourth, x + 17 = 54. Option A, 53, is the mean, not the median.
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