The arithmetic mean of $1, 2, 2, 3, 3, 3, ... n$ times ... – Statistics

Statisticshard · Past Paper

The arithmetic mean of $1, 2, 2, 3, 3, 3, ... n$ times $n$ is:

A$(n+1)/2$

B$(2n+1)/3$

C$n(n+1)/2$

D$n$

✓ Correct Answer: B — $(2n+1)/3$

Sum = $\sum n^2 = n(n+1)(2n+1)/6$. Total count = $\sum n = n(n+1)/2$. Mean = $(2n+1)/3$.

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