Question 867865: Find the standard deviation. Round to one more place than the data.
1, 2, 7, 20, 6, 7, 19, 8, 20
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Here's a summary of what we have to do and all of our steps
Step 1) Find the sample mean.
Step 2) Subtract the mean from each data element.
Step 3) Square each difference from step 2.
Step 4) Add up those squares from step 3.
Step 5) Divide that last result from step 3 by n-1 to get the sample variance.
Step 6) Take the square root of the sample variance to get the sample standard deviation.
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Step 1) Find the sample mean. Add up all the numbers
1+2+7+20+6+7+19+8+20 = 90
then divide by 9 (since there are 9 numbers in the list)
90/9 = 10
The sample mean is 10
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Step 2) Subtract the mean from each data element
1-10 = -9
2-10 = -8
7-10 = -3
20-10 = 10
6-10 = -4
7-10 = -3
19-10 = 9
8-10 = -2
20-10 = 10
The differences are: -9, -8, -3, 10, -4, -3, 9, -2, 10
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Step 3) Square each difference from step 2
(-9)^2 = 81
(-8)^2 = 64
(-3)^2 = 9
(10)^2 = 100
(-4)^2 = 16
(-3)^2 = 9
(9)^2 = 81
(-2)^2 = 4
(10)^2 = 100
The differences squared are: 81,64,9,100,16,9,81,4,100
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Step 4) Add up those squares from step 3
81+64+9+100+16+9+81+4+100 = 464
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Step 5) Divide that last result from step 3 by n-1 = 9-1 = 8
464/8 = 58
This value is the sample variance. If you want the population variance (which leads to the population standard deviation), then you divide by n = 9 instead of n-1 = 8. Since you'll usually use the sample standard deviation in most cases, we'll stick with this.
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Step 6) Take the square root of 58 to get sqrt(58) = 7.61577310586391 this value is approximate.
So the sample standard deviation is approximately 7.61577310586391
Round this to 1 decimal place to get the final answer of 7.6
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