Here are the number of hours that each of a group of students studied for this exam:

2 4 22 6 1 4 1 5 7 4

What is the standard deviation of the number of study hours?
Answer 5.8
6.1
37.2
33.4
56

After finding the mean I then found the sum of all numbers divided that by the numbers minus one and got 6.09 which is 6.1 rounded up. Is this correct?

If the 10 data points were randomly selected from a larger group of data, then you use N-1 in the denominator. This calculation gives a "sample standard deviation." The formula for sample standard deviation is:


s = \sqrt { \frac 1 {N-1} \displaystyle \sum_ {i=1} ^N (x_i - \bar x ) ^2 }


But if in fact there are only 10 data points in total for the complete population, then you determine the standard deviation of the full population using N in the denominator, not N-1:


\sigma = \sqrt { \frac 1 N \displaystyle \sum_ {i=1} ^N (x_i - \mu ) ^2 }


For this problem you should be using this second formula, since there were exactly 10 students. So you have:


\sigma = \sqrt { \frac 1 {10} \left( (2-5.6)^2 + (4-5.6)^2 + (22-5.6)^2 + ... + (4-5.6)^2 \right ) }