what is the standard deviation for 9,11,9,11,11,12,14?

Question

round answer to the nearest hundreth

Answer 1

Hello,

To find the standard deviation, we first have to find the mean: (9 + 11 + 9 + 11 + 11 + 12 +14)/7 = 11.
Then, we subtract the mean from each number to get the deviations from the mean:
9 - 11 = -2
11 - 11 = 0
9 - 11 = -2
11 - 11 = 0
11 - 11 = 0
12 - 11 = 1
14 - 11 = 3

Then we square each of those deviations and add them together: 4 + 0 + 4 + 0 + 0 + 1 + 9 =18.
The next part will depend on whether you want the sample standard deviation or the population standard deviation.

Sample:
Then we divide by the number of cases minus one - in your question, 7 - 1 = 6. This gives us 18/6 = 3. The last thing we do is take the square root: sqrt(3) = 1.73. So, in this case the standard deviation is 1.73

 

Population:

If you need the population standard deviation, you divide by the number of cases - in your question, 7 instead of 6. This give us 18/7 = 2.57. The  we take the square root: sqrt(2.57) = 1.60.

 

Hope that helps