Descriptive Statistics Calculator
Paste your data and get a complete statistical summary in one click — mean, median, mode, standard deviation, variance, quartiles, range, skewness, kurtosis, and more, with a live histogram and box plot.
Textbook-accurate formulas · Reviewed July 2026 · Methods aligned with the NIST Engineering Statistics Handbook
Enter Your Data
Works with commas, spaces, tabs, or line breaks. Decimals and negatives are fine.
Choose Sample if your data is a subset of a larger group (most common). Choose Population if it includes every member.
Statistical Summary
Distribution Histogram
Enter data to see the distribution
- Frequency
- Mean
- Median
Box Plot (Five-Number Summary)
| Enter numbers to see the full summary | — |
What Is Descriptive Statistics?
Descriptive statistics is the branch of statistics that summarizes and describes the main features of a dataset. Instead of listing every raw number, it condenses your data into a handful of meaningful figures — a typical value, how spread out the numbers are, and what shape the distribution takes. This calculator computes the entire descriptive summary at once, so you can understand your data at a glance rather than crunching each measure by hand.
These measures fall into four families: central tendency (where the center is), dispersion (how spread out the data is), position (where specific values sit), and shape (how symmetric or peaked the distribution is). Together they paint a full picture of what your numbers are really telling you.
Measures of Central Tendency
Central tendency answers a simple question: what’s a typical value? There are three common measures, and each tells a slightly different story.
- Mean — the arithmetic average, found by adding all values and dividing by the count. It’s the most familiar measure but can be pulled off-center by outliers.
- Median — the middle value when data is sorted. It’s resistant to outliers, which makes it the better choice for skewed data like incomes or house prices.
- Mode — the value that appears most often. A dataset can have one mode, several modes, or none at all.
Measures of Dispersion (Spread)
Two datasets can share the same mean yet look completely different. Dispersion measures capture that difference — how tightly or loosely the values cluster around the center.
- Range — the simplest measure: the maximum minus the minimum.
- Variance — the average of the squared distances from the mean.
- Standard deviation — the square root of the variance, expressed in the original units. For a deeper dive, use our dedicated Standard Deviation Calculator.
- Interquartile range (IQR) — the spread of the middle 50% of your data (Q3 − Q1), which ignores extreme values.
- Mean absolute deviation — the average absolute distance of each value from the mean.
Measures of Position: Quartiles & the Five-Number Summary
Quartiles split your sorted data into four equal parts. The first quartile (Q1) marks the 25th percentile, the second (Q2) is the median, and the third (Q3) is the 75th percentile. Together with the minimum and maximum, they form the five-number summary — the basis for the box plot shown in the results above. The box plot is one of the fastest ways to visually spot the center, spread, and any outliers in your data.
How this calculator finds quartiles
This tool uses the widely taught median-of-halves method (also called the exclusive method). It first finds the median to split the data into a lower and upper half, then takes the median of each half to get Q1 and Q3. This is the same approach used in most textbooks and by calculators like CalculatorSoup. Note that different software (Excel’s two QUARTILE functions, for example) may use slightly different interpolation methods, so results can vary marginally.
Measures of Shape: Skewness & Kurtosis
Skewness measures the asymmetry of your distribution. A skewness near zero means the data is roughly symmetric. Positive skew means a longer tail on the right (the mean sits above the median); negative skew means a longer tail on the left (the mean sits below the median). Kurtosis measures the weight of the tails relative to a normal distribution. This calculator reports excess kurtosis, where zero matches a normal bell curve, positive values indicate heavier tails and more outliers, and negative values indicate lighter tails.
| Measure | What it tells you | Category |
|---|---|---|
| Mean | The arithmetic average value | Central tendency |
| Median | The middle value; robust to outliers | Central tendency |
| Mode | The most frequent value(s) | Central tendency |
| Standard deviation | Typical distance from the mean | Dispersion |
| Variance | Average squared distance from the mean | Dispersion |
| IQR | Spread of the middle 50% of data | Position |
| Skewness | Asymmetry of the distribution | Shape |
| Kurtosis | Tail heaviness vs. a normal curve | Shape |
How to Use This Descriptive Statistics Calculator
- Paste your data into the box — separated by commas, spaces, or new lines.
- Choose sample or population depending on whether your data is a subset or the whole group.
- Read your results instantly — key stats appear on top, with the full summary, histogram, and box plot below.
- Copy or print the results for your report, homework, or spreadsheet.
Frequently Asked Questions
It computes a full statistical summary of a dataset in one step, including measures of central tendency (mean, median, mode), dispersion (standard deviation, variance, range, IQR), position (quartiles and the five-number summary), and shape (skewness and kurtosis). Instead of calculating each by hand, you paste your numbers and get every measure at once, along with a histogram and box plot to visualize the data.
Descriptive statistics summarize and describe the data you actually have — its center, spread, and shape. Inferential statistics go a step further, using a sample to draw conclusions or make predictions about a larger population, through tools like confidence intervals and hypothesis tests. This calculator focuses on descriptive statistics; it tells you about your dataset, not a wider population.
Choose sample (divide by n − 1) when your data is a subset representing a larger group you can’t fully measure — this is the most common case. Choose population (divide by N) only when your data includes every member of the group you care about. The choice affects the variance, standard deviation, and related measures. When unsure, sample is the safer default, and it’s selected here by default.
The five-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. These five values describe the center and spread of your data and are used to draw a box plot. They’re especially useful for skewed data because, unlike the mean and standard deviation, they aren’t distorted by extreme values.
For skewness, a value near zero means symmetric data, positive means a longer right tail (mean above median), and negative means a longer left tail (mean below median). As a rough guide, skewness between −0.5 and 0.5 is fairly symmetric, while beyond ±1 is highly skewed. For excess kurtosis, zero matches a normal distribution, positive indicates heavier tails with more outliers, and negative indicates lighter tails.
There are several accepted methods for calculating quartiles, and they can give slightly different results, especially for small datasets. This calculator uses the median-of-halves (exclusive) method common in textbooks. Excel offers both an inclusive method (QUARTILE.INC) and an exclusive one (QUARTILE.EXC), and statistical software may use other interpolation rules. None is “wrong” — they’re just different conventions, and the differences shrink as your dataset grows.
Methodology & formulas used
This calculator uses standard textbook formulas, reviewed July 2026. All computation runs locally in your browser and your data is never uploaded.
- Mean: x̄ = Σxᵢ / n
- Median: middle value of the sorted data (average of the two middle values if n is even)
- Mode: the most frequently occurring value(s)
- Sample variance: s² = Σ(xᵢ − x̄)² / (n − 1); population uses ÷ N
- Standard deviation: square root of the variance
- Quartiles: median-of-halves (exclusive) method; IQR = Q3 − Q1
- Outlier fences: Q1 − 1.5×IQR and Q3 + 1.5×IQR
- Skewness (sample): Fisher-Pearson standardized moment coefficient, requires n > 2
- Excess kurtosis (sample): fourth standardized moment minus 3, requires n > 3
- Standard error: SE = s / √n
Estimates are for educational and planning purposes. Quartile, skewness, and kurtosis conventions vary between software packages; see the FAQ for details.
References
- NIST/SEMATECH. Measures of Skewness and Kurtosis — e-Handbook of Statistical Methods. itl.nist.gov
- NIST/SEMATECH. Summary Statistics — Location and Scale. itl.nist.gov/div898/handbook
- Bessel’s Correction — n − 1 for unbiased sample variance. en.wikipedia.org