# Standard Deviation

• Nov 26th 2009, 10:57 AM
chungkayan
Standard Deviation
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?
• Nov 26th 2009, 05:50 PM
Robb
Quote:

Originally Posted by chungkayan
any idea how to work out the standard deviation?

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

So
$
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
• Dec 3rd 2009, 12:38 PM
chungkayan
Thanks for the help. I get it now. this is the formula for working every standard deviation sum, right?