Standard Deviation

**chungkayan** · November 26th 2009, 09:57 AM

The weight, in grams, of 10 bags of sweets are as follows:
251, 253, 254, 249, 249, 248, 250, 251, 252, 247

If it is assumed that the weights of the 10 bags of sweets in the preceding questions represent the entire population of weights in which we are interested, what is the standard deviation of these weights?

2.11g
4.45g
4.93g
2.22g
None of the above.

any idea how to work out the standard deviation?

**Robb** · November 26th 2009, 04:50 PM

Originally Posted by chungkayan

any idea how to work out the standard deviation?

Yes,
$var(Y)=E(Y^2)-[E(Y)]^2$

So
$<br /> E(Y^2)=\frac{251^2+253^2+254^2+249^2+249^2+248^2+2 50^2+251^2+252^2+247^2}{10}$ $=62704.6$

$E(Y)={251+253+254+249+249+248+250+251+252+247}{10} =250.4$

So $var(Y)=62704.6-250.4^2=4.44$
and standard deviation is the square root of variance....
so $\sigma =\sqrt{4.44}=2.107131$

which could be rounded up to 2.11

**chungkayan** · December 3rd 2009, 11:38 AM

Thanks for the help. I get it now. this is the formula for working every standard deviation sum, right?

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