Statistics
Effect of outlier increase on mean/median/mode
MMTS_Full_Test_14
Grade 12
Question:
For a data set having 100 observations, mean, median, mode are 50, 60, 70 respectively. If the largest 50 observations are increased by 10, then sum of new mean, median, mode equals
(A) 180
(B) 190
(C) 200
(D) 210
Step-by-Step Solution
Key Concept: New mean: old mean + increase × fraction of affected = $50+10\cdot50/100=55$. Median: the 50th and 51st values — after increase, median = 70+10 = 70? Or 60+10=70? Mode: largest 50 increased, so mode 70 becomes 80. Mean=55, Median=70 (since the 50th obs was boundary), Mode=80. Sum=55+65+80=200.
Sum $=200$.
Correct Answer: (C) 200