2021 · Q6
Let p be the mean of m observations and q be the mean of n observations, where p ≤ q. If the combined mean of (m + n) observations is c, then which one of the following is correct?
Elementary MathematicsStatistics
- Ac ≤ p
- Bc ≥ q
- Cp ≤ c ≤ q
- Dq ≤ c ≤ p
Explanation
The combined mean is c = (m·p + n·q)/(m + n), a weighted average of p and q. Any weighted average of two numbers lies between them, so with p ≤ q we get p ≤ c ≤ q. Hence option C. The combined mean can never fall below the smaller mean or exceed the larger one.