# Math Help - Mean of a Set of Numbers

1. ## Mean of a Set of Numbers

Hello. I recently encountered this question on a math test, and it totally stumped me.

The mean of a set of numbers is 0.40. The sum of the numbers is 56. How many numbers are in the set?

I guessed 14 (completely random guess). The correct answer turned out to be 140. It was a multiple choice question, but I forgot what the other two choices were.

I know that when somebody tells me how to figure it out, it'll seem really dumb and obvious, but I just can't see how to right now. It's the only question on the test that I had no idea how to solve. Any help that anyone could give me would be greatly appreciated!

2. Originally Posted by greenstupor
Hello. I recently encountered this question on a math test, and it totally stumped me.

The mean of a set of numbers is 0.40. The sum of the numbers is 56. How many numbers are in the set?

I guessed 14 (completely random guess). The correct answer turned out to be 140. It was a multiple choice question, but I forgot what the other two choices were.

I know that when somebody tells me how to figure it out, it'll seem really dumb and obvious, but I just can't see how to right now. It's the only question on the test that I had no idea how to solve. Any help that anyone could give me would be greatly appreciated!
How do we find the mean?

For a given set of numbers,

$\mbox {mean} = \frac { \mbox {sum of the numbers } }{ \mbox {the number of numbers we have} }$

$\Rightarrow \mbox { the number of numbers there are } = \frac { \mbox { sum of the numbers} }{ \mbox {mean } }$

So here, $\mbox {the number of numbers there are } = \frac {56}{0.4} = 140$

3. That's totally amazing. I never thought of such a brilliant method.

4. Originally Posted by Jonboy
That's totally amazing. I never thought of such a brilliant method.
Hmmm, "brilliant" huh? well, i guess, maybe. I didn't think it was that big o' deal, all i did was transpose the formula for the mean

5. Originally Posted by Jhevon
Hmmm, "brilliant" huh? well, i guess, maybe. I didn't think it was that big a deal, all i did was transpose the formula for the mean
I've seen a problem like this on my ACT and I had not a clue to solve it. I would of never thought of writing out what the mean was and transposing it. That's neat.

6. Originally Posted by Jonboy
I've seen a problem like this on my ACT and I had not a clue to solve it. I would of never thought of writing out what the mean was and transposing it. That's neat.
I totally agree. I never would've thought to do that on my own. Thanks so much for the help!