What Is Mean and Stdev?
Stdev is the common spreadsheet shorthand for standard deviation. Excel and Google Sheets offer two main versions: STDEV.S for a sample and STDEV.P for a whole population. Picking the wrong one is the most common mistake.
Paste your values to get the mean, both stdev values, both variances, the count, the sum and the standard error. A table beside the results lists the spreadsheet function and the calculator key for each.
The sections below explain the difference between STDEV.S and STDEV.P, give a worked example and answer common questions about the older STDEV and STDEVP names.
How to Use the Mean and Stdev Calculator
- Enter your numbers.
- Read the mean and both stdev values.
- Use the table to find the matching spreadsheet function.
- Check the dot plot and histogram for outliers.
Mean and Stdev Formula
Sample stdev (STDEV.S)
Population stdev (STDEV.P)
Mean and Stdev Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| x̄ | Mean of the values | |
| n | Number of values | |
| s | Sample stdev, STDEV.S | divides by n − 1 |
| σ | Population stdev, STDEV.P | divides by n |
Mean and Stdev Worked Example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared deviations sum to 32. STDEV.P is √(32 ÷ 8) = 2 and STDEV.S is √(32 ÷ 7) = 2.138.
With the example values loaded in the calculator above, the steps are:
- Mean = SUM ÷ COUNT = 150 ÷ 10 = 15.
- STDEV.S (sample) divides the squared deviations by n − 1 = 9: 2.5819889.
- STDEV.P (population) divides by n = 10: 2.4494897.
Result: Mean (AVERAGE) = 15; Sample stdev (STDEV.S) = 2.5819889; Population stdev (STDEV.P) = 2.4494897.
How to Read the Mean and Standard Deviation
The mean gives the centre and the standard deviation gives the typical distance from it. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5. The squared deviations total 32, so the population standard deviation is √(32 ÷ 8) = 2 and the sample standard deviation is √(32 ÷ 7) ≈ 2.138.
Spreadsheets use different functions for these two. STDEV.S is the sample version and STDEV.P is the population version, and the table on this page maps each result to its spreadsheet name.
Where Mean and Stdev Is Used
Spreadsheet checks
Compare your results with AVERAGE, STDEV.S and STDEV.P to be sure you used the right function.
Lab data
Summarise repeated measurements with a mean and standard deviation.
Quick standard error
Get stdev ÷ √n from the same list.
Homework
Confirm a hand calculation of the squared deviations.
Common Mean and Stdev Mistakes to Avoid
- Use STDEV.S unless your list is the entire population.
- Older spreadsheets use STDEV, which is the same as STDEV.S.
- The mean and standard deviation can mislead on strongly skewed data. Look at the median as well.
- Enter the numbers separated by commas, spaces or new lines.
Mean and Stdev Terms and Definitions
- stdev
- Short for standard deviation.
- Range
- In a spreadsheet, the block of cells holding your data.
Mean and Stdev FAQs
What is the difference between STDEV.S and STDEV.P?
STDEV.S divides by n − 1 and estimates the standard deviation of a population from a sample. STDEV.P divides by n and treats the data as the whole population. For 2, 4, 4, 4, 5, 5, 7, 9 they give 2.138 and 2.
How do I calculate mean and stdev in Excel?
Use =AVERAGE(range) for the mean, =STDEV.S(range) for the sample standard deviation and =STDEV.P(range) for the population value.
Which stdev should I use?
Use the sample version when your data are a sample of a larger group, which is the usual case. Use the population version only when you have every value.
Is STDEV the same as STDEV.S?
Yes. STDEV is the older name and gives the same sample standard deviation as STDEV.S.