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 ?

Correct option is B

Solution:
Step 1: Median Calculation
Original Data: 110, 41, 43, 95, 127, 99, 61, 92, 71, 93, 110, 36.
Sorted Data: 36, 41, 43, 61, 71, 92, 93, 95, 99, 110, 110, 127.
Old Median = (92+93)/2 =185/2 = 92.5
New Data: 110, 41, 43, 95, 127, 99, 61, 92, 71, 94, 110, 36.
Sorted New Data: 36, 41, 43, 61, 71, 92, 94, 95, 99, 110, 110, 127.
New Median = (92+94)/2 = 186/2 = 93
Difference in Median:
Difference = 93 − 92.5 = 0.5
Statement 1 is incorrect.
Step 2: Mean Calculation
Old Mean:
Sum of original data = 110+41+43+95+127+99+61+92+71+93+110+36 = 978
Old Mean= 978/12 = 81.5
New Mean:
Sum of new data=110+41+43+95+127+99+61+92+71+94+110+36 = 979
New Mean = 979/12 ≈ 81.583
Difference in Mean: Difference=81.583−81.5 = 0.083
Statement 2 is correct (the difference is less than 0.1).
Step 3: Mode Calculation
Old Mode: 110 (appears twice)
New Mode: 110 (still appears twice)
Difference in Mode: Zero.
Statement 3 is correct.
Therefore, the correct statements are: Ans. (b) 2 and 3 only