A researcher has a median "p" for the data set 15, 12, 14, 28, 16, 28, 32, 36, 13, 12, 34, 39. If the 16 is replaced by 19, and 13 by 31 in the above data set, then the median of the resulting data set is "q". The arithmetic mean of "p" and "q" is:
- A. 28
- B. 25 ✓
- C. 50
- D. 56
Correct Answer: B. 25
Explanation
Initial sorted set (12 values): 12, 12, 13, 14, 15, 16, 28, 28, 32, 34, 36, 39. Median p = \frac{16+28}{2} = 22. New sorted set (replacing 16 with 19, 13 with 31): 12, 12, 14, 15, 19, 28, 28, 31, 32, 34, 36, 39. Median q = \frac{28+28}{2} = 28. Mean of p and q = \frac{22+28}{2} = 25.