Center
Mean, median, and mode for the typical value or most common value in your data.
Free statistics calculator
Descriptive Statistics Calculator for Mean, SD, Variance, and IQR
Paste raw data into this descriptive statistics calculator to calculate mean, median, mode, range, quartiles, five-number summary, IQR, variance, standard deviation, standard error, coefficient of variation, and outlier fences. Choose sample or population calculations where the denominator matters.
- Raw data input Paste numbers separated by commas, spaces, semicolons, or new lines.
- Sample option Uses n - 1 for sample variance and sample standard deviation.
- Population option Uses N for population variance and population standard deviation.
- Full summary Includes center, spread, five-number summary, and sorted values.
Calculate Descriptive Statistics From Raw Data
Enter your dataset below. Use the sample setting for most class datasets, surveys, experiments, and research samples. Use population only when the values are the complete population you want to describe.
Separate values with commas, spaces, semicolons, or line breaks. Use decimal points for decimals. Numbers written with thousands commas, like 1,000, are read as a single value.
Results
Sample descriptive statistics
Count
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Sum
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Mean
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Median
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Mode
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Minimum
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Maximum
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Range
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Q1
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Q3
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IQR
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Lower Outlier Fence
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Upper Outlier Fence
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Potential Outliers
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Variance
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Standard Deviation
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Standard Error
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Coefficient of Variation
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Five-Number Summary
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Sorted Data
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Quartiles use the median-of-halves method. For formal coursework, follow the quartile method requested by your instructor or software output. Standard error is shown in sample mode. Coefficient of variation is shown only for a positive mean; it is most useful for ratio-scale data with a meaningful zero.
What This Calculator Includes
Descriptive statistics summarize what is in a dataset before you move into inference, hypothesis tests, regression, ANOVA, or written interpretation.
Spread
Range, variance, standard deviation, standard error, and coefficient of variation.
Position
Minimum, Q1, Q3, maximum, IQR, and outlier fence checks using quartiles.
Sample or population
Choose sample calculations when your data represent part of a larger population.
Sample vs Population Standard Deviation
The sample and population choice changes variance, standard deviation, and coefficient of variation. Standard error is shown only in sample mode. The choice does not change count, sum, mean, median, mode, minimum, maximum, range, Q1, Q3, or IQR.
| Measure | Formula idea | When to use it |
|---|---|---|
| Sample variance | sum((x - x-bar)^2) / (n - 1) |
Use when your data are a sample and you want to estimate population variation. |
| Population variance | sum((x - mean)^2) / N |
Use when your dataset includes every value in the population being described. |
| Standard deviation | sqrt(variance) |
Use to describe typical distance from the mean in original data units. |
| Standard error | sample standard deviation / sqrt(n) |
Use with a sample to estimate uncertainty in its mean. It is not reported here when the values are marked as the complete population. |
Common Mistakes to Avoid
- Using population standard deviation when the data are only a sample from a larger group.
- Reporting the mean for highly skewed data without also checking the median and IQR.
- Forgetting that sample variance and sample standard deviation use n - 1 in the denominator.
- Copying calculator output into a report without explaining what the numbers mean in context.
Descriptive Statistics Calculator FAQs
Is this also a standard deviation calculator?
Yes. It calculates standard deviation, variance, mean, median, mode, range, quartiles, IQR, standard error, coefficient of variation, and the five-number summary from the same raw data input.
Should I choose sample or population?
Choose sample when your data represent part of a larger population, which is common in homework, surveys, experiments, and research datasets. Choose population only when the values include every member of the group being described.
Why are sample and population standard deviation different?
Sample standard deviation uses n - 1 in the denominator to estimate variation in a larger population. Population standard deviation uses N because it describes the full population directly.
Can I use these results in Excel, SPSS, R, or Stata assignments?
You can use the calculator to check individual values, but your final assignment should still follow the required software method, show the correct output, and explain the results in context.
Need Help Interpreting the Results?
A calculator can give the numbers, but your assignment may also require a method choice, written interpretation, software output, outlier discussion, or a clear explanation of what the descriptive statistics mean for the question.
Related Statistics Help
Use Calculators Responsibly
Use this calculator to check work, learn formulas, and prepare questions for tutoring. For graded assignments, follow your course rules and cite or explain calculations as required.