Ask Me Help Desk - Standard deviation

Hello,

can you please explain me how to calculate standard deviation in this example?

The following data were sampled from a population with sample size n=815

litter size frequency
1 7
2 33
3 58
4 116
5 125
6 126
7 121
8 107
9 56
10 37
11 25
12 4

First, I calculated the mean (1*7+2*33+3*58+... +12*4)/815=6.125
Then I calculated standard deviation, but my result was wrong and the teacher just gave me the answer s=2.2756 without explanation. I tried to recalculate, but there was no luck.
Please help me
Thanks

Well standard deviation is represented by the function

$s=\frac{sqrt{\sum_{i=1}^n(x_i-\overline{x})^2}}{n-1}$ where $\overline{x}$ is the mean, and $x_i$ is the sample you are taking the difference of.

We should have:

$s=sqrt{\frac{7(1-6.125)^2+33(2-6.125)^2+58(3-6.125)^2+116(4-6.125)^2+125(5-6.125)^2+126(6-6.125)^2+121(7-6.125)^2+107(8-6.125)^2+56(9-6.125)^2+37(10-6.125)^2+25(11-6.125)^2+4(12-6.125)^2}{814}$

Which does indeed end up being about 2.2756

whoa that's a bit of a mouthful.

Thank you very much!

Got it!