There are a few steps involved which will follow this basic outline
Step 1) Find the sample mean (xbar)
Step 2) Subtract the xbar value from each data point. This list is the set of deviations from the mean.
Step 3) Square each result found in step 2. This list is the set of squared deviations from the mean.
Step 4) Add up the results found in step 3. This value is known as the sum of the squared deviations
Step 5) Divide the value found in the previous step by n = 10 to yield the population variance
Step 6) Apply the square root to the population variance to get the population standard deviation
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Step 1) Find the sample mean xbar
Add up the values. Divide the sum by 10 (since there are n = 10 values)
xbar = (Sum of the values)/10
xbar = (75+80+90+95+75+85+55+80+90+95)/10
xbar = 820/10
xbar = 82
The sample mean is xbar = 82
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Step 2) Subtract the sample mean from EVERY data value to form a new list
75-82 = -7
80-82 = -2
90-82 = 8
95-82 = 13
75-82 = -7
85-82 = 3
55-82 = -27
80-82 = -2
90-82 = 8
95-82 = 13
The differences are: -7, -2, 8, 13, -7, 3, -27, -2, 8, 13
This new list {-7, -2, 8, 13, -7, 3, -27, -2, 8, 13} is the list of deviations from the mean
In other words, it's the list of differences from the mean.
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Step 3) Square each result found in step 2 to get the list of squared deviations
(-7)^2 = 49
(-2)^2 = 4
(8)^2 = 64
(13)^2 = 169
(-7)^2 = 49
(3)^2 = 9
(-27)^2 = 729
(-2)^2 = 4
(8)^2 = 64
(13)^2 = 169
The results from above are: 49, 4, 64, 169, 49, 9, 729, 4, 64, 169
The list of squared deviations from the mean is {49, 4, 64, 169, 49, 9, 729, 4, 64, 169}
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Step 4) Add up each result found in the previous step to get the sum of the squared deviations.
49+4+64+169+49+9+729+4+64+169 = 1310
The sum of the squared deviations is equal to 1310
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Step 5) Divide the sum of the squared deviations (1310) by n = 10 to get 1310/10 = 131
The population variance is 131
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Step 6) Take the square root of population variance 131 to get sqrt(131) = 11.4455231422596
The population standard deviation is 11.4455231422596
Round that to the nearest tenth to get 11.4
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Final Answer: 11.4