Standard deviation from grades distribution how am I wrong?

[Femme_physics]

Homework Statement

The grades distribution in class is

10, 8, 8, 7, 7, 7, 6, 6, 4

What's the standard deviation?

The Attempt at a Solution

I found the average is 7 (which is true) and used the formula for standard deviation. I checked it twice on the calculator but I'm still getting the same score, which is wrong. Anyone have a clue?

http://img135.imageshack.us/img135/6773/standarddev.jpg

 

[I like Serena]

Hey

I found the average is 7 (which is true) and used the formula for standard deviation. I checked it twice on the calculator but I'm still getting the same score, which is wrong. Anyone have a clue?

What formula do you have for the standard deviation?

You need to divide the sum of squares by the number of grades minus one, before you draw the square root.

 

[Femme_physics]

Maybe I have the wrong formula. The formula is what I used that you see. Each grade minus the average squared, all under a square root.

The sum of the squares is 22.
The sum of all grades minus one is 8
The square root of 22/8 is 1.658

The answer book is going for 1.563

 

[Mark44]

Also, there's not a single standard deviation. There's the population standard deviation and there's the sample standard deviation. The formulas for these are different, with sample standard deviation always being a bit larger. The one that I like Serena alluded to is the sample standard deviation.

 

[I like Serena]

Maybe I have the wrong formula. The formula is what I used that you see. Each grade minus the average squared, all under a square root.

The sum of the squares is 22.
The sum of all grades minus one is 8
The square root of 22/8 is 1.658

The answer book is going for 1.563

You will have the wrong formula then.

What the answer book will have done, is to divide the sum of squares by the number of grades.
[edit] That is the square root of 22/9 [/edit]

This is actually the wrong answer, but it'll do for now, until we get to the fine points of standard deviations.

 

[Mark44]

Maybe I have the wrong formula. The formula is what I used that you see. Each grade minus the average squared, all under a square root.

The sum of the squares is 22.
The sum of all grades minus one is 8
The square root of 22/8 is 1.658

That's what I'm getting, too. I don't see anything wrong in what you did. You might check to make sure that the data you show is the same as given in the problem. If it is, I suspect a wrong answer in the book.

The answer book is going for 1.563

 

[Femme_physics]

Good enough for me :) Thanks, great helpers!

 

[Ray Vickson]

Maybe I have the wrong formula. The formula is what I used that you see. Each grade minus the average squared, all under a square root.

The sum of the squares is 22.
The sum of all grades minus one is 8
The square root of 22/8 is 1.658

The answer book is going for 1.563

std = sqrt(v), where v = variance. We have v = sum[(x-m)^2,i=1..n)]/n, where m = mean = sum(x,i=1..n)/n. In your case n = 9, and calculation gives m = 7, so v = 22/9, hence std = sqrt(22/9) = 1.564, approx.

RGV