Standard Deviation result wrong or right

Question

I made two scripts in PHP to calculate the standard deviation. But I am not sure if it works correctly both of my scripts have different results.

first script 1,2,3,4,5,1 = 1.5

second script 1,2,3,4,5,1 = 1.49

or are both wrong if so please tell me what the standard deviation is. Thanks!

After the edit there is not really a discrepancy between the result, is it? — Hagen von Eitzen, Feb 19 '14 at 22:19
I edited just before you posted your answer, apologies for that. — Raymond the Developer, Feb 19 '14 at 22:24

score 2 · Accepted Answer · answered Feb 19 '14 at 22:19

2

The average of your data is $$ \bar x = \frac{1+2+3+4+5+1}{6}=\frac83.$$ Thus $$s_n^2=\frac1n\sum(x_i-\bar x)^2= \frac16\left(\frac{25}{9}+\frac49+\frac19+\frac{16}9+\frac{49}{9}+\frac{25}{9}\right)=\frac{20}{9}$$ and $$s_{n-1}^2=\frac1{n-1}\sum(x_i-\bar x)^2=\frac 83.$$ This makes $$s_n\approx 1.4907\qquad s_{n-1}\approx 1.63299 $$ It seems you are calculating $s_n$ and just use different rounding.

answered Feb 19 '14 at 22:19

Hagen von Eitzen

374,180

It seems that the second script works. Really appreciate your answer. Thanks! – Raymond the Developer Feb 19 '14 at 22:26

score 0 · Answer 2 · answered Feb 19 '14 at 22:20

0

With these few values, you can just run the calculation by hand. Alpha gives $\frac {2\sqrt 5}3 \approx 1.4907$

answered Feb 19 '14 at 22:20

Ross Millikan

374,822

That's a nice shortcut. I asked this question because I don't know much about math only coding. The script I made was for a client that wanted the standard deviation for a score system. Before today I never even heard of it. – Raymond the Developer Feb 19 '14 at 22:31

Standard Deviation result wrong or right

2 Answers2