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Calculators / Math / Standard deviation
Standard deviation calculator
Calculate population mean, variance and standard deviation for five values.
On this page
Mean3.34
Population variance0.7
Population standard deviation0.84
Calculator controls
How to calculate
Calculate population mean, variance and standard deviation for five values.
Mean = (a+b+c+d+e)/5; Population variance = ((a-(a+b+c+d+e)/5)^2+(b-(a+b+c+d+e)/5)^2+(c-(a+b+c+d+e)/5)^2+(d-(a+b+c+d+e)/5)^2+(e-(a+b+c+d+e)/5)^2)/5; Population standard deviation = sqrt(((a-(a+b+c+d+e)/5)^2+(b-(a+b+c+d+e)/5)^2+(c-(a+b+c+d+e)/5)^2+(d-(a+b+c+d+e)/5)^2+(e-(a+b+c+d+e)/5)^2)/5)
Worked example
Value 1: 2; Value 2: 4; Value 3: 4; Value 4: 4; Value 5: 5.
Mean: 3.34 ; Population variance: 0.7 ; Population standard deviation: 0.84 .
Assumptions and limits
This page uses the population denominator of five. A sample standard deviation uses n−1 instead.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate population mean, variance and standard deviation for five values. The displayed figures use the inputs and formula shown on this page.
When this tool is useful
Use the standard deviation to compare a scenario, check an estimate, or verify a manual calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Value 1 | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Value 2 | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Value 3 | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Value 4 | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Value 5 | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What should I check before using the standard deviation result?
This page uses the population denominator of five. A sample standard deviation uses n−1 instead.
Is this standard deviation result exact?
It is exact for the stated mathematical model and entered values. Real-world results can differ when rates, timing, fees, definitions or measurement conditions differ.