How the heck do you find the stantard deviation?

Question

Please help me....Im so frustrated....
These are the 18 numbers....

7.1

9.2

8.0

6.1

14.4

8.5

6.1

6.8

7.7

21.5

6.7

9.0

8.4

7.0

11.5

14.1

9.5


8.6

Please help me...From my understanding you must find the mean....then you subtract the numbers to the mean, and add up the difference and divide it by 18...Why do i keep getting different answers...

10 PTS TO THE first correct answer.....Thanks.

SORRY for the title and my language ;)

I'm so frustrated..

SORRY for the title and my language ;)

I'm so frustrated..

Answer 1

You've almost got it. For the standard deviation, you must subtract each number from the mean, and then square that value. Then add all these 18 values together, divide by 18 (or 17 if this is a sample and not a population), then take the square root of that number.

I won't show all of my work on here because it's too lengthy, but the standard deviations are below

For a sample (/17): 3.852000584

For a population (/18): 3.743471684

Here's an example of what to do:

After calculating the mean of the data set (9.4555556), take each value and subtract the mean, then square it.

First one:

(7.1 - 9.455555556)² = 5.548641975

Do this for the other 17 values, add them up, divide by 17 or 18 and then take the square root.

Answer 2

An alternative method for calculating σ can be derived as follows:
m = (Σx)/n
σ = √((Σ(m - x)^2)/n)
σ = √((Σm^2 - 2mΣx + Σx^2)/n)
σ = √((nm^2 - 2mnm + Σx^2)/n)
σ = √((Σx^2)/n - m^2)
. x . . . . x^2
. 7.1 ... 50.41
. 9.2 ... 84.64
. 8.0 ... 64
. 6.1 ... 37.21
14.4 . 207.36
. 8.5 ... 72.25
. 6.1 ... 37.21
. 6.8 ... 46.24
. 7.7 ... 59.29
21.5 . 462.25
. 6.7 ... 44.89
. 9.0 ... 81
. 8.4 ... 70.56
. 7.0 ... 49
11.5 . 132.25
14.1 . 198.81
. 9.5 ... 90.25
. 8.6 ... 73.96
Σx = 170.2, Σx^2 = 1861.58
m = 170.2/18 ≈ 9.455555556
(Σx^2)/n = 1861.58/18 ≈ 103.4211111
103.4211111 - 89.4075309 = 14.01358025
σ = √14.01358025 ≈ 3.7434717

Answer 3

this site should help.

www.animatedsoftware.com/statglos/sgstdev.htm