Two datasets A and B have the same mean. Which of the following MUST be true?

Sum of the observations in A = Sum of the observations in B.

Solution

Given :-

Two datasets A and B have the same mean

Formula Used:-

$Mean=\frac {\text Sum of observation}{\text Number of Observation}$ 

Solution:-

Given: Two dataset A and B have the same mean.

If the sizes of A and B are different, their sums can differ.
NOT necessarily true.

Same mean does not imply the same mean of squares.
Example: A=[2,4], B=[3,3].
NOT necessarily true.

Combined mean = weighted mean of
A and B.
It does not equal mean of A+ mean of B
NOT true.

Combined mean = mean of A, because both datasets have the same mean.
MUST be true.

Thus, the correct answer is option (D)If the two datasets are combined, then the mean of the combined dataset = mean of A.

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