Consider the following data: 110, 41, 43, 95, 127, 99, 61, 92, 71, 93, 110, 36. If 93 is replaced by 94, then consider the following statements: 1. The difference between new median and old median is 1. 2. The difference between new mean and old mean is less than 0.1. 3. The difference between new mode and old mode is zero. Which of the statements given above are correct?
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Explanation
The 12 observations sort to a median of (92 + 93)/2 = 92.5; replacing 93 by 94 moves the median to (92 + 94)/2 = 93, a difference of 0.5 rather than 1, so statement 1 is false. The total rises by 1, so the mean rises by 1/12 ≈ 0.083 < 0.1, making statement 2 true. The mode stays 110 (it occurs twice in both sets), so statement 3 is true. Hence “2 and 3 only”, option (b).