# Thread: Explanation of formula to calcuate group data

1. ## Explanation of formula to calcuate group data

I just need an explanation of what's going on in the formula. The formula is used in statistics for calculating the mean for grouped data in a table. My question is: how do arrive I at the square root of 13.942? I have a graphing calculator and I still was not able to obtain s= 3.7 minutes. I took a picture of the formula and posted the link at the bottom. Any help is appreciated thank you in advance.

http://postimg.org/image/6b8d92o7v/

if the link is dead, I will try to re-post it manually.

2. If I understand what you're asking correctly... these are notes you took while your instructor worked a problem. You wrote down his/her steps but don't quite understand them. If this is not what you're having difficulty with, please correct me.

Assuming it is, then you're having trouble after the notes hit this step:

$S=\frac{\sqrt{130464-112896}}{36\left(35\right)}$

Well, let's try a few intermediate steps to hopefully clarify. If we subtract the two terms under the square root, we get:

$S=\frac{\sqrt{17568}}{36\left(35\right)}$

Now, you know that you can simply a square root by pulling out a perfect square. So does 17568 divide by any perfect squares? It does. And the largest of those is 144. That means we can pull out a 12 from the square root.

$S=\frac{12\sqrt{122}}{36\left(35\right)}$
$S=\frac{\sqrt{122}}{105}$

Now if I were solving this problem, I'd stop here and use an exact form. But if you want to approximate, we can do that. And then we realize that... whoops. This problem doesn't work out the way your notes say it should. Hence why even with a calculator you were getting a different answer. So, either you copied the notes down wrong, or your instructor messed up.

3. Nope. I copied it from a textbook and everything is on point. I posted the picture of the exact text at the bottom.

http://postimg.org/image/6brvsm7sv/

4. Okay, thank you for posting the clarification. I understand what happened now. There was a very small error in copying it down, and it's a fairly simple one to overlook. What you wrote in your notes, and thus what I worked through in my earlier post starts with:

$S=\frac{\sqrt{n\left(\sum \:x^2f\right)-\left(\sum \:xf\right)^2}}{n\left(n-1\right)}$

where only the numerator is under the square root. However, the picture from your book starts with this formula:

$S=\sqrt{\frac{n\left(\sum \:\:x^2f\right)-\left(\sum \:\:xf\right)^2}{n\left(n-1\right)}}$

where the entire fraction is under the square root. Do you see why that makes a difference? Try solving it now and see what you get :)

5. I just now see the difference but I still can't find out how the textbook arrives at the square root of 13.942...

The way I was doing it before was performing the subtraction of 130,463 and 112,896 and dividing it by 36(35) and getting 20,704. I squared root it and got 143.9...

Then I tried finding the square root of the numerator and denominator as you suggested and I got 132.544 / 35.496 which gives me 3.734 and that's great because that's the answer!

BUT... I just don't see how the textbook arrives at the square root of 13.942... but you were very helpful thanks! I'll just play with the numbers and take it from there.