Concept:Central tendency measures (median, mean, mode) change when data is altered, and we compute the differences.
Explanation:Old data (unsorted): 110, 41, 43, 95, 127, 99, 61, 92, 71, 93, 110, 36.
Old sorted (12 values): 36, 41, 43, 61, 71, 92, 93, 95, 99, 110, 110, 127.
New data: replace 93 with 94. Sorted new: 36, 41, 43, 61, 71, 92, 94, 95, 99, 110, 110, 127.
Statement 1:Old median (average of 6th and 7th) =
(92+93)/2=92.5.
New median =
(92+94)/2=93.
Difference =
93−92.5=0.5, not 1. So statement 1 is false.
Statement 2:Old mean = sum of old values / 12 =
(36+41+43+61+71+92+93+95+99+110+110+127)/12=978/12=81.5.
New mean = (old sum + 1)/12 =
979/12≈81.5833.
Difference =
81.5833−81.5=0.0833<0.1. So statement 2 is true.
Statement 3:Old mode = 110 (occurs twice).
New mode = 110 (still occurs twice).
Difference =
110−110=0. So statement 3 is true.
Correct statements are 2 and 3 only.
Answer:Option B (2 and 3 only).