Standard deviation calculator
Paste your numbers and get the standard deviation, variance and more, with the working.
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How to use Standard deviation calculator
- Paste your numbers
- Choose sample or population
- Read the results and steps
Separate numbers with commas, spaces, semicolons or new lines.
Sample standard deviation
Enter some numbers to see the standard deviation, mean, median and more.
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How to use Standard deviation calculator
Paste your numbers
Type or paste values separated by commas, spaces, semicolons or new lines, such as a column copied from a spreadsheet.
Choose sample or population
Pick sample for part of a group and population for every value. Both results are always shown.
Read the results and steps
See the standard deviation, variance, mean, median, mode, range and a table of each value’s deviation from the mean.
Why use Utils365
Sample and population
Both standard deviations and variances side by side, so you never use the wrong formula.
Every summary statistic
Count, sum, mean, median, mode, minimum, maximum and range from the same list.
Working you can follow
A table shows x, x − mean and (x − mean)² for every value, with the totals used in the formula.
Your number style
Decimal commas work in languages that use them, so 1,5 is read as one and a half.
Frequently asked questions
How do you calculate standard deviation?
Find the mean, subtract it from each value and square the result, add the squares, divide by n (population) or n − 1 (sample), then take the square root. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population SD is 2.
What is the difference between sample and population standard deviation?
Population SD divides by n and is for when you have every value. Sample SD divides by n − 1 to correct for estimating from part of a group. For 2, 4, 4, 4, 5, 5, 7, 9 they are 2 and about 2.138.
Which one should I use?
Use sample when your numbers are a selection from a bigger group, such as survey answers or test results from some students. Use population when you have the whole group.
What is variance?
The average of the squared differences from the mean, so the standard deviation squared. A standard deviation of 2 means a variance of 4.
What does a high standard deviation mean?
That values are spread far from the mean. In a normal distribution about 68% of values lie within one SD of the mean and about 95% within two.
How is the median found?
Sort the values and take the middle one. With an even count, take the mean of the two middle values: the median of 2, 4, 4, 4, 5, 5, 7, 9 is (4 + 5) ÷ 2 = 4.5.
Can I paste numbers from Excel or Google Sheets?
Yes. Copy a column or row and paste it in. New lines, tabs, spaces, commas and semicolons all separate values, and anything that isn’t a number is skipped and listed.