Question

The mean of the data
set is 15. What number
is missing?
18, 16, ____, 9, 12, 23​

Answer 1

12

Explanation:

The Mean is the average of the numbers: a calculated "central" value of a set of numbers.

To calculate it:

• add up all the numbers,

• then divide by how many numbers there are.

`mean=(a_1+a_2+a_3+...+a_n)/(n)`

We have: 18, 16, x, 9, 12, 23 - six numbers (n = 6) and mean = 15.

Substitute:

`(18+16+x+9+12+23)/(6)=15\\\\(78+x)/(6)=15\qquad\text{multiply both sides by 6}\\\\6\!\!\!\!\diagup\cdot(78+x)/(6\!\!\!\!\diagup)=(6)(15)\\\\78+x=90\qquad\text{subtract 78 from both sides}\\\\78-78+x=90-78\\\\x=12`