Question

The mean of the increasing ordered set of numbers, {6, x, 22}, is equal to the median. What is the value of x?

Answer 1

`x=14`

Explanation:

The mean of a set is the sum of the value divided by the number of values.

And the median is the middle number.

First, let’s find the mean. We will have the sum of:

`6+x+22`

And this will be divided by 3, the number of elements. Hence, the mean is:

`(28+x)/(3)`

This is equivalent to the median, in this case x.

Therefore, our equation is equal to x:

`(28+x)/(3)=x`

Solve for x. Multiply both sides by 3:

`28+x=3x`

Subtract x from both sides:

`2x=28`

Divide both sides by 2:

`x=14`

Hence, the value of x is 14.