How to Compute Population Standard Deviation Without Using a Computer Program
The statistical term standard deviation refers to the dispersion of data about a mean (average) value. You can find the standard deviation of a sample of data or the standard deviation of an entire population. A sample is a subset of a population. The formulas for sample standard deviation and population standard deviation differ slightly, but the procedure used to obtain the result is the same.
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Instructions
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1
Make a table with six rows and four columns. In row one, put the column headings. Column 1 is Number. Column 2 is Mean of All Numbers in Set. Column 3 is Number - Mean of All Numbers in Set. Column 4 is (Number - Mean of All Numbers in Set) Squared.
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2
Start filling in the table. The numbers used here are examples. Any numbers will work. In column 1, put the numbers 6, 4, 7, 8, 0.
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3
In Column 2, write the mean or average of 6, 4, 7, 8, and 0 in every blank. 6 plus 4 plus 7 plus 8 plus 0 divided by 5 equals 5, so write 5 in each blank.
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4
In column 3, compute Number minus Mean, meaning column 1 minus column 2. Going down, you should have 1, -1, 2, 3, -5.
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5
In column 4, compute (Number - Mean) squared. Going down, you should have 1, 1, 4, 9, 25.
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6
Add the numbers obtained in Column 4. The result is 40.
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7
Divide your answer in step 6 by 5, the number of entries. The result is 8.
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8
Take the square root of your answer in step 7. You get 2.83 for your final answer.
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Tips & Warnings
Don't confuse population standard deviation with sample standard deviation. If you were doing sample standard deviation, step 7 would be slightly different, causing a different final answer in step 8.
