SOLUTION: Find the sample standard deviation. 22 29 21 24 27 28 25 36

Algebra ->  Average -> SOLUTION: Find the sample standard deviation. 22 29 21 24 27 28 25 36      Log On


   

Question 1133608: Find the sample standard deviation.
22 29 21 24 27 28 25 36
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Standard Deviation,
22 ,29 ,21, 24 ,27, 28, 25 ,36
First, work out the average, or arithmetic mean, of the numbers:
mu=%2822%2B29%2B21%2B24%2B27%2B28%2B25+%2B36%29%2F8=26.5
N+=8
Then, take each number, subtract the mean and square the result:
22-26.5=-4.5
29-26.5=2.5
21-26.5=-5.5
24-26.5=-2.5
27-26.5=0.5
28-26.5=1.5
25+-26.5=-1.5
36-26.5=+9.5
Square of each difference:
%28-4.5%29%5E2, 2.5%5E2,+%28-5.5%29%5E2, %28-2.5%29%5E2,+0.5%5E2, 1.5%5E2,+%28-1.5%29%5E2, 9.5%5E2=20.25, 6.25, 30.25,+6.25, 0.25, 2.25, 2.25, 90.25
Now calculate the Variance:
add up the squared differences and divide by count
%2820.25%2B6.25%2B30.25%2B+6.25%2B+0.25%2B+2.25%2B+2.25%2B90.25%29%2F8=158%2F8=19.75
Lastly, take the square root of the Variance:

sqrt%2819.75%29=4.444097209->the sample standard deviation