Find the average when zero is also there

Question

If a set $A = \{0,1,10\}$ . What is the average?

Is it $\frac{(0+1+10)}{3}$ or $\frac{(1+10)}{2}$.

Answer 1

The former. 0 is still an element of your set $A$ and hence has to be accounted for.

Answer 2

The mean of a multiset of $n$ numbers, $\{a_1,a_2,a_3,\dots,a_n\}$ is defined as

$$\mu = \frac{a_1+a_2+\dots+a_n}{n}$$

This is regardless of whether or not some of the elements in the set are zero, repeated, negative, or otherwise uncommon for whatever reason.

Examples:

The average of $\{1,3,5\}$ is $\frac{1+3+5}{3}=\frac{9}{3}=3$

The average of $\{-5,1,4,6\}$ is $\frac{(-5)+1+4+6}{4} = \frac{6}{4}=1.5$

The average of $\{1,1,1,5\}$ is $\frac{1+1+1+5}{4} = \frac{8}{4}=2$

The average of $\{0,1,10\}$ is $\frac{0+1+10}{3} = \frac{11}{3}$