Skill: Find a missing value given the mean

The mean is the equal-share value of a data set. To find a missing value:

1. Count the total number of values.
2. Multiply the mean by the number of values to find the total.
3. Add the known values.
4. Subtract the known total from the overall total.

Example

The mean of five numbers is $8$. Four of the numbers are $(6, 9, 7,)$ and $(10)$. What is the missing number?

Step 1: Find the total of all five numbers.

$$5 \times 8 = 40$$

So, all five numbers together must total $(40)$.

Step 2: Add the known numbers.

$$6+9+7+10=32$$

Step 3: Subtract to find the missing number.

$$40-32=8$$

The missing number is $\boxed{8}$.

Check: The numbers are $(6, 9, 7, 10,)$ and $8$. Their total is $(40)$, and

$$40 \div 5=8$$

so the mean is correct.