Descriptive Statistics Calculator
Get the mean, median, mode, range, quartiles, standard deviation, variance, standard error, coefficient of variation and skewness of your data in one go, with a clear step-by-step solution.
Descriptive Statistics Calculator
Enter your numbers below and get a full summary of your data instantly.
Step-by-Step Solution
What Are Descriptive Statistics?
Descriptive statistics are numbers that summarize a data set. Instead of reading every value, you can use a few key figures to see where the data is centered, how spread out it is, and what shape it has.
They are usually grouped into three kinds of measures:
- Center: the mean, median and mode.
- Spread: the range, interquartile range, variance, standard deviation, standard error and coefficient of variation.
- Shape and position: the minimum, maximum, quartiles and skewness.
What This Calculator Shows
For any list of numbers, our calculator finds all of the following at once. Each name links to a calculator that explains it in more detail.
- Count and sum: how many values there are and what they add up to.
- Mean: the sum divided by the count. See the Average Calculator.
- Median: the middle value after sorting. See the Median Calculator.
- Mode: the most frequent value. See the Mode Calculator.
- Minimum, maximum and range: the smallest value, the largest value and the gap between them. See the Range Calculator.
- Q1, Q3 and IQR: the quartiles and the spread of the middle half of the data. See the Quartile Calculator.
- Variance and standard deviation: how far values typically are from the mean. See the Variance Calculator and the Standard Deviation Calculator.
- Standard error: how precisely the sample mean estimates the true mean. See the Standard Error Calculator.
- Coefficient of variation: the standard deviation as a percentage of the mean. See the Coefficient of Variation Calculator.
- Skewness: whether the data leans to one side.
The quartiles in this calculator use the median-of-halves method, where the median is left out of both halves for an odd number of values. If you need another method, use the Quartile Calculator.
For the spread of your data, see the Standard Deviation Calculator, and for the precision of the mean, the Standard Error Calculator.
Descriptive Statistics Examples
Example 1: a small data set (sample)
Count = 8, sum = 40 and mean = 5. The median is 4.5 and the mode is 4. The minimum is 2, the maximum is 9 and the range is 7. Q1 = 4, Q3 = 6 and the IQR is 2. The sample variance is about 4.5714, the sample standard deviation is about 2.1381, and the standard error is about 0.7559. The coefficient of variation is about 42.7618%.
Example 2: evenly spread data (sample)
Count = 5, sum = 150 and mean = 30. The median is 30 and there is no mode. The range is 40, Q1 = 15, Q3 = 45 and the IQR is 30. The sample variance is 250 and the sample standard deviation is about 15.8114. Because the data is perfectly symmetric, the skewness is 0.
How to Read Skewness
Skewness describes the shape of your data.
- Close to 0: the data is roughly symmetric, with similar spread on both sides of the mean.
- Positive: the data has a longer tail on the high side. A few large values pull the mean above the median.
- Negative: the data has a longer tail on the low side. A few small values pull the mean below the median.
As a rough guide, many people call data fairly symmetric when the skewness is between −0.5 and 0.5. Skewness needs at least three values, and with very small data sets it is not reliable.
Sample or Population?
Choose population when your data includes every member of the group you care about. Choose sample when your data is only a part of a larger group, which is the most common case.
The sample option divides by n − 1 when it finds the variance, and uses a matching adjustment for the skewness. The population option divides by n. The count, sum, mean, median, mode, range and quartiles are the same either way.
More Descriptive Statistics Examples
These extra worked examples show what descriptive statistics look like for skewed data, for sample and population choices, for data with a mean of zero, and for comparing spread with the coefficient of variation. The quartiles here use the median-of-halves method, where the median is left out of both halves for an odd number of values.
Example 3: Data with one very large value
Find the descriptive statistics of 2, 3, 3, 4, 5, 6, 26, treated as a sample.
Answer: the mean is 7, but the median is only 4, and the skewness is positive.
Count = 7, sum = 49 and mean = 49 ÷ 7 = 7. The median is 4 and the mode is 3. The minimum is 2, the maximum is 26 and the range is 24. The lower half is 2, 3, 3 so Q1 = 3, and the upper half is 5, 6, 26 so Q3 = 6, which gives an IQR of 3. The deviations from the mean are −5, −4, −4, −3, −2, −1 and 19, and their squares add up to 432. The sample variance is 432 ÷ 6 = 72, the sample standard deviation is √72 ≈ 8.4853, and the standard error is 8.4853 ÷ √7 ≈ 3.2071. The coefficient of variation is 8.4853 ÷ 7 × 100 ≈ 121.2183%.
The single value 26 pulls the mean far above the median, which is the typical sign of positive skewness. In data like this, the median describes the center better than the mean, and the IQR describes the spread better than the standard deviation.
Example 4: Sample or population?
Find the variance and standard deviation of 2, 3, 5, 8, 12, first as a sample and then as a population.
Answer: the sample standard deviation is about 4.0620, and the population standard deviation is about 3.6332.
Count = 5, sum = 30 and mean = 6. The median is 5, the range is 10, Q1 = (2 + 3) ÷ 2 = 2.5, Q3 = (8 + 12) ÷ 2 = 10 and the IQR is 7.5. The deviations are −4, −3, −1, 2 and 6, and their squares add up to 66. Sample: the variance is 66 ÷ 4 = 16.5 and the standard deviation is √16.5 ≈ 4.0620. Population: the variance is 66 ÷ 5 = 13.2 and the standard deviation is √13.2 ≈ 3.6332. The count, sum, mean, median, range and quartiles are the same either way. Only the measures that use the variance change.
Example 5: Data with a mean of zero
Find the descriptive statistics of −4, −2, 0, 2, 4, treated as a sample.
Answer: the mean and the median are both 0, the skewness is 0, and the coefficient of variation is not available.
Count = 5 and sum = 0, so the mean is 0. The median is 0 and there is no mode. The range is 8, Q1 = (−4 + −2) ÷ 2 = −3, Q3 = (2 + 4) ÷ 2 = 3 and the IQR is 6. The squared deviations are 16, 4, 0, 4 and 16, which add up to 40, so the sample variance is 40 ÷ 4 = 10, the standard deviation is √10 ≈ 3.1623 and the standard error is 3.1623 ÷ √5 ≈ 1.4142. The data is perfectly symmetric, so the skewness is 0. The coefficient of variation divides by the mean, and a mean of 0 cannot be used, so it is not available.
Example 6: Comparing spread with the coefficient of variation
Group X has a mean of 50 and a standard deviation of 5. Group Y has a mean of 200 and a standard deviation of 10. Which group is more variable compared with its own average?
Answer: Group X is more variable relative to its mean, even though Group Y has the larger standard deviation.
Group X: the coefficient of variation is 5 ÷ 50 × 100 = 10%. Group Y: the coefficient of variation is 10 ÷ 200 × 100 = 5%. The standard deviation alone favors X, but relative to the size of the mean, Y is more consistent. For a deeper look at this measure, try our Coefficient of Variation Calculator.
Common mistakes when summarizing data
A common mistake is to look only at the mean. When the data has an extreme value, the median and the IQR are often more useful, as Example 3 shows. Another is choosing population when your numbers are only a part of a bigger group. Also remember that different tools use different quartile methods, so the quartiles may not match another tool exactly. To check just the middle value, use our Median Calculator.
Created by Sajid Ali, SmartStatCalc · Last updated: 7 November 2026
Found a mistake or have a suggestion? Contact us.
How to Use Our Descriptive Statistics Calculator
- Type or paste your numbers into the Data Values box.
- Choose sample or population.
- Click the Calculate Statistics button.
- Read the summary cards for each statistic.
- Use the step-by-step solution to see how each value was found.
Click Reset at any time to clear your data and start again.
Why Use SmartStatCalc?
SmartStatCalc is built to make everyday statistics quick and easy to understand. Instead of using many separate tools, you can paste your data once and get the full picture.
Who Can Use a Descriptive Statistics Calculator?
Students use it to check homework and to prepare data for reports. Teachers use it to summarize test scores, and researchers and analysts use it as a first look at a new data set before they run deeper tests.
Frequently Asked Questions
What are descriptive statistics?
They are summary numbers, such as the mean, median and standard deviation, that describe the main features of a data set.
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarize the data you have. Inferential statistics use a sample to draw conclusions about a larger group.
Which measures describe the center of the data?
The mean, median and mode all describe the center, each in a different way.
Which measures describe the spread of the data?
The range, interquartile range, variance, standard deviation and coefficient of variation describe how spread out the values are.
Why is the skewness missing or not available?
Skewness needs at least three values, and it cannot be found if every value is the same. In those cases the calculator shows that it is not available.
Why is the coefficient of variation not available?
The coefficient of variation divides by the mean, so it needs a mean greater than zero.
Should I choose sample or population?
Choose sample if your numbers are only a part of a bigger group, and population if they include every member.
Is this Descriptive Statistics Calculator free?
Yes. SmartStatCalc's Descriptive Statistics Calculator is free to use online.
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Cite this calculator
If you use this calculator in your work, you can cite it like this:
SmartStatCalc. (2026). Descriptive Statistics Calculator. https://smartstatcalc.com/descriptive-statistics-calculator/