Question 608181: An animal clinic kept record of the life spans of certain poodles. The number of years the dogs lived are 8, 10, 12, 15, 17, and 13. What is the standard deviation of the poodle life spans?
No other information is given and i am stuck.. Please help!!!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First, we need to find the sample mean
xbar = (8+10+12+15+17+13)/6 = 75/6 = 12.5
So the sample mean is xbar = 12.5
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Now subtract the sample mean from EVERY data value:
8-12.5 = -4.5
10-12.5 = -2.5
12-12.5 = -0.5
15-12.5 = 2.5
17-12.5 = 4.5
13-12.5 = 0.5
So the differences are: -4.5, -2.5, -0.5, 2.5, 4.5, 0.5
Now square each difference:
(-4.5)^2 = 20.25
(-2.5)^2 = 6.25
(-0.5)^2 = 0.25
(2.5)^2 = 6.25
(4.5)^2 = 20.25
(0.5)^2 = 0.25
Now add up each square:
20.25+6.25+0.25+6.25+20.25+0.25 = 53.5
Now divide that sum by n-1 = 6-1 = 5 to get 53.5/5 = 10.7
So the sample variance is 10.7
Finally, take the square root of 10.7 to get 3.27108544675923
So the sample standard deviation is 3.27108544675923
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