About Standard Deviation From a Frequency Table
This calculator finds the standard deviation of grouped data. Enter one value and its frequency per line, or a class interval such as 10-20 with its count. Class intervals are counted at their midpoint. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The mean is the sum of f times x divided by n, where n is the total frequency, and the sum of squares is the sum of f times (x - mean) squared. There is no need to write out the data as a long list.
With class intervals the answer is an estimate, because the true values inside each class are unknown and are all treated as the midpoint.
How to use Standard Deviation From a Frequency Table
- Paste or type your numbers, separated by commas, spaces or new lines. Use a dot for decimals.
- Pick Sample (n - 1) if the numbers are a sample, or Population (n) if they are the whole group.
- For grouped data, switch Data entry to Frequency table and enter one "value, frequency" pair per line. A class interval such as 10-20, 4 is counted at 15.
- Read the standard deviation at the top, then the variance, mean, sum, count, standard error and margin of error.
- Open the working and the deviations table to see each (x - mean) and its square, and the totals that feed the formula.
Features
- Sample and population standard deviation side by side, with the one you chose as the headline.
- Variance, mean, count, sum, range, standard error and margin of error at 90%, 95% or 99% confidence.
- Step-by-step working in written-out formulas, with a table of deviations and squared deviations.
- Frequency table and class interval input, with a weighted calculation instead of an expanded list.
- Coefficient of variation as a percentage of the mean.
- Copy the results as text. Works with long lists and on a phone.
Standard deviation of a frequency table
Weight every value by how often it occurs.
n = sum(f)
mean = sum(f x) / n
SS = sum(f (x - mean)^2)
s = sqrt(SS / (n - 1))Worked examples
Values 1 to 5 with counts 4, 7, 10, 6, 3 gives n = 30, mean 2.9, s = 1.1847
Same answer as listing the thirty values out.
Classes 0-10, 10-20, 20-30, 30-40 with counts 4, 9, 12, 5 gives Mean 21, s = 9.3218
The midpoints 5, 15, 25 and 35 stand in for each class.
Privacy: how it works
- All the arithmetic happens in your browser tab. The numbers you paste are not sent to Ulkaa or to any other server.
Tips
- One extreme value can inflate the standard deviation a lot. Check the deviations table for a very large squared deviation.
- Standard deviation has the same unit as your data. Variance is in squared units, which is harder to interpret.
- To compare spread between data sets with different means or units, use the coefficient of variation.
- A sample needs at least two values. With one value the sample standard deviation is undefined.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I enter class intervals?
Type the interval and the count, for example 10-20, 4. The calculator counts that class at 15.
Is the grouped answer exact?
Only for exact values. For class intervals it is an estimate, since the real values inside a class are not known.
More Standard Deviation Calculator pages
- Standard Deviation CalculatorPaste your numbers to get the sample or population standard deviation, the variance and the working.
- Sample Standard Deviation CalculatorPaste your numbers to get the sample standard deviation, which divides by n - 1.
- Population Standard Deviation CalculatorPaste the whole population to get the standard deviation sigma, which divides by n.
- Coefficient of Variation CalculatorPaste your numbers to get the coefficient of variation, the standard deviation as a percentage of the mean.