Consider the following data:<br>110, 41, 43, 95, 127, 99, 61, 92, 71, 93, 110, 36.<br>If 93 is replaced by 94, then consider the following statements:<br>1. The difference between new median and old median is 1.<br>2. The difference between new mean and old mean is less than 0.1.<br>3. The difference between new mode and old mode is zero.<br>Which of the statements given above are correct?
- A. 1 and 2 only
- B. 2 and 3 only ✓
- C. 1 and 3 only
- D. 1, 2 and 3
Correct Answer: B. 2 and 3 only
Explanation
Sorted data (old): 36, 41, 43, 61, 71, 92, 93, 95, 99, 110, 110, 127. Old median is (92+93)/2 = 92.5. With 94, new median is (92+94)/2 = 93. Difference is 0.5 \neq 1 (Statement 1 is false). Sum increases by 1, so mean increases by 1/12 \approx 0.083 \lt 0.1 (Statement 2 is true). Mode remains 110, so difference is zero (Statement 3 is true).
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