Standard Deviation stuff

Sorry the edit keeps messing it up...

The first "answer" I put Mean on top of, so the mean is 4

the 2nd "answer" I put Difference things on top of.

The charts are the difference thingys...

But from there I have absolutely NO IDEA what to do...

3,2,4,7

Find the standard deviation of the data set.
 Round your answer to the nearest hundredth.

Standard deviation of the sample

\(s^2=\frac{\sum(x_i-\overline x)^2}{n-1}\)

\(n=4\\ \overline x=4\)

\(s^2=\frac{(3-4)^2+(2-4)^2+(4-4)^2+(7-4)^2}{4-1}\\ s^2=\frac{1+4+0+9}{3}\\ s^2=\frac{14}{3}\)

\(s=\sqrt{\frac{14}{3}}\\ s=2.1602469\)

\(s\approx 2.16\)

  !

3,2,4,7

Find the standard deviation of the data set.
Round your answer to the nearest hundredth.

Standard deviation of the sample

\(s^2=\frac{\sum (x_i-\overline x)^2}{n-1}\)

\(n=4\\ \overline x=\frac{3+2+4+7}{4}\\ \overline x=4\)

\(s^2=\frac{(3-4)^2+(2-4)^2+(4-4)^2+(7-4)^2}{4-1}\\ s^2=\frac{1+4+0+9}{3}\\ s^2=\frac{14}{3}\\ s=\sqrt{\frac{14}{3}}=2.1602469\)

\(s\approx 2.16\)

Standard deviation of the population

\(s^2=\frac{\sum (x_i-\overline x)^2}{n}\)

\(s^2=\frac{(3-4)^2+(2-4)^2+(4-4)^2+(7-4)^2}{4}\\ s^2=\frac{1+4+0+9}{4}\\ s^2=\frac{14}{4}\\ s=\sqrt{\frac{14}{4}}=1.87083\)

\(s\approx 1.87\)

  !

I learned it using steps like above but you would continue it like this(found my math textbook yay)

:

Then you have to find the mean of the last column

(1+4+0+9)/4

14/4

7/2

then square root that to get 

sqrt(7/2)

and the answers sqrt(7/2)

which is around 1.87

(Textbook way, no formula...)

I think This problem was categorized terribly as it accepts the population answer.