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SillyWilly377 · Aug 4, 2010, 12:11 PM

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?

ebaines · Aug 4, 2010, 12:52 PM

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 ) } $