I need help finding the range and standard deviation of this data set

[somavera7]

Please take a look at the problem in the picture I have attached below.

It is asking me to find the range and standard deviation.

From what I know, the range is the biggest number minus the smallest number (127.6 - 84.9 = 42.7).

What I really don't understand how to calculate is the standard deviation. Even though I looked at a few examples online, it's still unclear to me how to get the correct answer.

Can you please explain to me all of the steps to finding the standard deviation so that I will also be able to solve similar problems on my own?



Thank you!

 

[tkhunny]

You have the Range.

For the Standard Deviation of the Sample Set, you'll need the Mean of the sample. Do that, first.

Please show YOUR work. The Range was good. Now, keep going.

 

[HallsofIvy]

The standard deviation is the "root mean square" of the deviation of the data from the mean. To find the standard deviation, first find the mean or average of the data. To find that, of course, add all the data and divide by 10. Now subtract that mean from each given number. Since the mean is a "center", about half the numbers you get will be positive, half negative and their average would be 0. To avoid that cancelling, square each one and add those squares, find their average by dividing by 9, not 10, and finally, take the square root.

(The reason for dividing by 9, not 10, has always been a little vague to me. IF the data set were the entire population, rather than a sample, we would divide by N, the size of the population. I have told myself that, because we are using a sample, we are not as accurate as if we were using the entire population so we take the standard deviation a little larger by dividing by N- 1 rather than N.)