# The average age of the seven P.E. teachers at Carl's school is 38. If the ages of six of them are 52, 30, 23, 28, 44, and 45, what is the age of the seventh teacher?

Jun 11, 2017

44

#### Explanation:

To calculate a mean of a set of data, add up all of the data and divide by the number of items of data.
Let the age of the seventh teach be $x$.
With that, the average of the teachers ages is calculated by:

$\frac{52 + 30 + 23 + 28 + 44 + 45 + x}{7} = 38$

Then we can multiply through by 7 to get:

$\frac{52 + 30 + 23 + 28 + 44 + 45 + x}{7} \times 7 = 38 \times 7$
$\implies 52 + 30 + 23 + 28 + 44 + 45 + x = 266$

The we subtract all of the other ages to get:

$x = 266 - 52 - 30 - 23 - 28 - 44 - 45 = 44$.