- A5, 12, 19.5, 28.5, 41
- B5, 11, 19.5, 30, 41
- C5, 12, 18, 28.5, 41
- D5, 14, 19.5, 27, 41
Step-by-Step Solution
The extremes are 5 and 41. With twelve readings the median is the mean of the 6th and 7th, (18 + 21)/2 = 19.5. The lower half is 5, 8, 11, 13, 14, 18, and being six values its median is again a mean of a middle pair, (11 + 13)/2 = 12; the upper half 21, 24, 27, 30, 34, 41 gives (27 + 30)/2 = 28.5. So the summary is 5, 12, 19.5, 28.5, 41. Picking single values at the 3rd and 10th places instead of averaging pairs gives 11 and 30; taking the 6th reading 18 as the median forgets that an even count has no single middle; and 14 and 27 come from counting the quartile positions from the wrong end of each half.
Answer: A) 5, 12, 19.5, 28.5, 41