2023 · Q10
If the median of observations 12, 1, 8, 54, 61, 28, 45, 35, 21, 17 is M, then what is the value of 2M + 5?
Elementary MathematicsStatistics
- A12
- B28
- C52
- D54
Explanation
The median of an even-sized data set is the average of the two middle values after sorting, so the first step is to arrange the ten observations in ascending order: 1, 8, 12, 17, 21, 28, 35, 45, 54, 61. The 5th and 6th values are 21 and 28, so M = (21 + 28)/2 = 24.5. Then 2M + 5 = 2(24.5) + 5 = 49 + 5 = 54. None of the smaller options (12, 28, 52) match this computation, so the answer is (D) 54.