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 ?
A.1 and 2 only
B.2 and 3 only✓ Correct
C.1 and 3 only
D.1, 2 and 3
Explanation
Sorted: 36, 41, 43, 61, 71, 92, 93, 95, 99, 110, 110, 127. Old median = (92+93)/2 = 92.5. After replacing 93 with 94: sorted 36, 41, 43, 61, 71, 92, 94, 95, 99, 110, 110, 127. New median = (92+94)/2 = 93. Difference = 0.5, not 1. So statement 1 is wrong. Mean changes by (94−93)/12 = 1/12 ≈ 0.083 < 0.1, so statement 2 is correct. Mode is 110 in both cases (unchanged), so statement 3 is correct. Hence 2 and 3 only.
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