How to Find a Missing Value from the Mean

Problem

\text{mean } 12 \text{ of } 10,\ 13,\ 15,\ x

Answer

x = 10

A missing value problem runs the mean formula backwards. Build the total the mean implies, then subtract everything you already know.

Step-by-step solution

Find the total the mean describes.
$\text{total} = \text{mean} \times \text{count} = 12 \times 4 = 48$
Why: The mean equals the total divided by the count, so the total is the mean times the count.
Add the known values.
$10 + 13 + 15 = 38$
Why: The known values already use part of the total.
Subtract to find the missing value.
$x = 48 - 38 = 10$
Why: The missing value makes up the rest of the total.
Check the mean.
$\frac{10 + 13 + 15 + 10}{4} = \frac{48}{4} = 12$
Why: The check confirms the mean matches the given value.

Subtracting the mean from the sum of known values. Multiply the mean by the count first.
Forgetting to count the missing value in the total.
Dividing the sum of the known values by 3 and calling it the missing value.

Use the same method. Work each problem on paper, then open the answer to check.