Question

If the mean of 3, 3, 7, 8, 10, `x`, and `x` is 7, what is `x`?

Answer 1

`x=11`

Explanation:

Your question isn't very clear, but I think you mean. If the mean of 3, 3, 7, 8, 10, x is 7. What is x?

The mean is the sum of all the numbers divided by how many numbers you have.

So sum of 3, 3, 7, 8, 10,x:

`3+3+7+8+10+x= 31 +x`

We have 6 numbers,(including the x) so:

`(31 +x)/6`

And this is equal to 7:

`(31+x)/6=7`

Solving for `x`

Multiply both sides by `6`:

`31+x= 42`

Subtract 31 from both sides:

`x= 11`

Answer 2

`x=9`.

Explanation:

For any data set, the mean `mu` is calculated by adding the elements of the set together, and dividing this sum by the number of elements, `n`.

This is written generically as

`mu = (x_1+x_2+x_3+...+x_n)/n`

Given the data set `{3,3,7,8,10,x,x}` which has `n=7` elements, and that the mean of this data set is `mu = 7`, we can write the formula as

`color(white)0 7 = (3+3+7+8+10+x+x)/7`

and then solve for `x`:

`color(white)0 7 = (31+2x)/7`

`49=31+2x`

`18=color(white)(31+)2x`

`color(white)0 9=x`

So `x=9`; that is, the two remaining elements of the data set are both 9's.