SOLUTION: Please help me find the standard deviation of the data values: 10, 12, 12, 15, 16, 16, 16, 17, 19, 20

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Question 89828: Please help me find the standard deviation of the data values:
10, 12, 12, 15, 16, 16, 16, 17, 19, 20
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First find the mean

To find the mean, add up all of the numbers and divide the sum by the number of numbers (which in this case is 10).
Mean=%2810%2B+12%2B+12%2B+15%2B+16%2B+16%2B+16%2B+17%2B+19%2B+20%29%2F10=153%2F10=15.3

So the mean is 15.3



Now use this formula to find the standard deviation:

Standard Deviation: where is the arithmetic mean, is the ith number, and is the number of numbers

So we can replace N with 10



Replace with 15.3



Expand the summation (replace each x%5Bi%5D with the respective number)




Subtract the terms in the parenthesis



Square each term



Add up all of the terms

sqrt%28%281%2F10%2990.1%29

Multiply

sqrt%289.01%29

Take the square root

3.00166620396073

So the standard deviation is 3.00166620396073

You can verify this with any calculator that has stats functions.