Question

Find the standard deviation of the set of numbers.38, 47, 43, 44, 44, 41, 44The range is 9The standard deviation is___(Round to the nearest tenth as needed.)

Answer 1

Your data set is

`\lbrace38,41,43,44,44,44,47\rbrace`

Now, according to the range rule, the standard deviation is approximately equal to the range of the data divided by 4, i.e.

`\sigma\approx(9)/(4)=2.25`

It is only and estimation, and it is not always the best way to find it. So, I'll do it by finding first the mean and by using the equation for the standard deviation.

`\bar{x}\text{ }=(38+41+43+44+44+44+47)/(7)=43`

Then

`\sigma=\sqrt{(1)/(7)((38-43)²+(41-43)²+3(44-43)²+(47-43)²}=\sqrt{(1)/(7)(25+4+3+16)}=\sqrt{(48)/(7)}`

Then the standard deviation is

`\sigma=4\sqrt{(3)/(7)}\approx2.62`