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

Concept:

Arithmetic mean = sum of observations / total number of observations

Explanation:

Two datasets A and B have the same mean

Let observations of A are 2, 4, 6 and observations of B are 4, 4

So mean of A =  = 4 and mean of B =  = 4

So mean of A = mean of B

(1): sum of observations in A = 2 + 4 + 6 = 12 and sum of observations in B = 4 + 4 = 8, so not equal

Option (1) is false

(2): Mean of the squares of the observations in A =  = 28

and mean of the squares of the observations in B =  = 16

so both are not equation.

Option (2) is false

(3): If the two datasets are combined, then the mean of the combined dataset =  = 4

and mean of A + mean of B = 4 + 4 = 8

both are not equal

Option (3) is false

Given mean of A = mean of B 

So if the two datasets are combined, then the mean of the combined dataset = mean of A = mean of B

Option (4) is correct