The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?
Answer
The correct answer is A: 2.25. If each observation x is transformed to (x - 5)/20, the new mean becomes (Mean - 5)/20. Substituting Mean = 50: new mean = (50 - 5)/20 = 45/20 = 2.25.
A.2.25✓ Correct
B.3.5
C.4.25
D.5.5
Explanation
If each observation x is transformed to (x - 5)/20, the new mean becomes (Mean - 5)/20. Substituting Mean = 50: new mean = (50 - 5)/20 = 45/20 = 2.25.
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