Arithmetic mean

Question

 In a certain school, two teachers earn $16,000 per year, 3 teachers earn $17,000 per year, and 5 teachers earn $18,000 per year. What is the average annual salary of these teachers?

Answer 1

The arithmetic mean, or average, means to add up each of your values and divide by the number of values.

You'll take 2 - $16,000, 3 - $17,000, and 5 - $18,000 and get a total.  Then divide that total by 10, the number of salaries you are given.

 

$16,000 + $16,000 + $17,000 + $17,000 + $17,000 + $18,000 +$18,000 +$18,000 +$18,000 +$18,000  = $173,000.  Divided by 10 = $17,300.

 

In other words, teachers don't make enough money!

Answer 2

The first thing you can do is estimate the answer. 2 teachers earn $16,000, 3 teachers earn $17,000, and 5 teachers earn $18,000. If 2 teachers earn $16,000 and 2 teachers earn $18,000, the average is $17,000. That leaves 3 teachers earning $17,000 and 3 teachers earning $18,000. Therefore the average of these teachers would be $17,500. So we estimate that the average salary will be a little more than $17,000.

Solution: 2*$16,000=$32,000, 3*$17,000=$51,000, and 5*$18,000=$90,000

$32,000+$51,000+$90,000=$173,000

divide $173,000 by 10 because there are 10 teachers

$173,000/10=$17,300 average salary, and we estimated a little more than $17,000

answer: $17,300 average salary