# Find the variance and standard deviation of this set of data?

• Aug 6th 2007, 04:23 AM
princess_anna57
Find the variance and standard deviation of this set of data?
16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37
• Aug 6th 2007, 05:00 AM
topsquark
Quote:

Originally Posted by princess_anna57
16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

$\sigma ^2 = \frac{1}{N} \sum_{n = 1}^N (\bar{x} - x_n)^2$ <-- variance
where $\bar{x} = \frac{1}{N} \sum_{n = 1}^Nx_n$

and

$\sigma = \sqrt{\frac{1}{N} \sum_{n = 1}^N (\bar{x} - x_n)^2}$ <-- standard deviation

Depending on the kind of statistic you are trying to work with the $\frac{1}{N}$ might be a $\frac{1}{N - 1}$. You'll have to check your text or your notes to make sure.

So the first thing to is to calculate the average, $\bar{x}$, then use that to find the variance.

-Dan
• Aug 6th 2007, 05:20 AM
princess_anna57
The mean is 26.73. Now what do I do? ^_^

It's 1/N by the way.
• Aug 6th 2007, 05:47 AM
topsquark
Quote:

Originally Posted by princess_anna57
16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

Quote:

Originally Posted by princess_anna57
The mean is 26.73. Now what do I do? ^_^

It's 1/N by the way.

Now tabulate $(\bar{x} - x_n)^2$ for all the data points, then add them. Then divide by N and you have the variance.

This is where something like Excel comes in handy...

-Dan
• Aug 6th 2007, 05:58 AM
princess_anna57
Cool beans. How about the standard deviation?
• Aug 6th 2007, 06:19 AM
topsquark
Quote:

Originally Posted by princess_anna57
Cool beans. How about the standard deviation?

Take a look at the symbol I used for the variance, $\sigma ^2$. (This may not be a Universal notation, but it is standard in the two books I own.)

So to get the standard deviation $\sigma$ from the variance, just take the square root.

-Dan