Descriptive Statistics Calculator
Every summary statistic of your data, with a box plot, histogram and stem-and-leaf.
Statistics
These are the last results worked out. Fix the data above to update them.
Five-number summary
| Minimum | Q1 | Median | Q3 | Maximum |
|---|---|---|---|---|
Box: Q1 to Q3 with the median · whiskers: to the most extreme values inside the fences · ◆ mean · ○ mild outlier · ● extreme outlier.
All statistics
Percentiles
| Percentile | Value |
|---|
Frequency table
| Class | Midpoint | Frequency | Relative | Cumulative | Cumulative % |
|---|
Stem-and-leaf plot
About the Descriptive Statistics Calculator
Paste a list of numbers — or upload a CSV, TSV or Excel file and pick a column — and get every summary statistic at once: count, sum, mean, median, mode, range, sample and population variance and standard deviation, standard error, quartiles and any percentiles, the IQR, Tukey’s fences and the outliers, the five-number summary, skewness and kurtosis.
Quartiles and percentiles can be calculated in several standard ways, and programs disagree, so you choose the method: Excel’s PERCENTILE.INC or PERCENTILE.EXC, any of the nine Hyndman–Fan types used by R, or the median-of-halves rule taught in many schools, with or without the median. The data is also drawn as a box plot and a histogram — with Sturges, Freedman–Diaconis, Scott, square-root or Rice classes, or your own class width — and listed as a stem-and-leaf plot and a grouped frequency table with relative and cumulative frequencies. Everything is computed in your browser; nothing is uploaded.
How to use it
- Paste or type your numbers, separated by commas, spaces or new lines — or choose a CSV, TSV or Excel file and pick the column.
- Choose the quartile and percentile method (Excel PERCENTILE.INC is the default, as in Google Sheets and R) and the percentiles you want.
- Choose how the histogram classes are made, or set your own class width and starting point.
- Read the statistics, charts and tables. Copy the results, or download the report, the frequency table (CSV) or a chart (SVG).
Examples
2, 4, 4, 4, 5, 5, 7, 9
mean 5, σ = 2, s ≈ 2.1381
Σ(x − 5)² = 32, so σ² = 32/8 = 4 and s² = 32/7 ≈ 4.5714.
6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
Q1 = 25.5 (Excel .INC) or 15 (median of halves, Excel .EXC)
Q3 is 42.5 or 43. Choose the method your course or software uses.
1, 2, 3, 4, 5, 6, 7, 8, 9, 100
100 is an extreme outlier
Q1 = 3.25, Q3 = 7.75 and IQR = 4.5 (type 7), so the outer fence is 7.75 + 3 × 4.5 = 21.25.
3, 4, 5, 2, 3, 4, 5, 6, 4, 7
SKEW 0.3595, KURT −0.1518
Excel’s SKEW and KURT are the adjusted Fisher–Pearson forms G1 and G2.
Common uses
- Statistics homework: the five-number summary, box plot, stem-and-leaf plot and frequency table for a data set.
- Checking a spreadsheet: the same quartiles, SD, SKEW and KURT as Excel, with the method stated.
- A quick look at survey answers, test marks, sensor readings or sales figures before deeper analysis.
- Finding outliers with Tukey’s fences before computing averages.
Sample or population?
Use the sample variance and standard deviation, which divide by n − 1, when your data is a sample from a larger group whose spread you want to estimate. Use the population versions, which divide by n, when the data is the whole group. The standard error of the mean, s/√n, says how precisely the sample mean estimates the mean of the whole group.
Quartile and percentile methods
A percentile is a value below which a given share of the data falls, but with a finite sample there are several ways to interpolate; Hyndman and Fan (1996) list nine. Type 7, at position 1 + (n − 1)p in the sorted data, is used by Excel’s PERCENTILE.INC and QUARTILE.INC, Google Sheets, R and NumPy. Type 6, at position (n + 1)p, is used by Excel’s PERCENTILE.EXC, Minitab, SPSS and the NIST/SEMATECH e-Handbook; Excel’s .EXC gives #NUM! when that position is below 1 or above n, and the tool says so instead of guessing. School textbooks and TI-83/84 calculators often take Q1 and Q3 as the medians of the lower and upper halves of the data. Every method gives the same median; on small samples the quartiles can differ noticeably.
Outliers and the box plot
The box spans Q1 to Q3 with a line at the median, and the diamond marks the mean. The whiskers reach the most extreme values inside the inner fences, Q1 − 1.5·IQR and Q3 + 1.5·IQR (Tukey, 1977). Points beyond the inner fences are mild outliers (hollow circles) and points beyond the outer fences, Q1 − 3·IQR and Q3 + 3·IQR, are extreme outliers (filled), as in the NIST/SEMATECH e-Handbook. The fences use the quartiles of the method you choose.
Skewness and kurtosis
Joanes and Gill (1998) compare three common forms. With mᵣ = Σ(x − x̄)ʳ/n, the classical moment forms are g1 = m₃/m₂^(3/2) and g2 = m₄/m₂² − 3. The adjusted forms used by Excel (SKEW and KURT), SAS and SPSS are G1 = g1·√(n(n − 1))/(n − 2) and G2 = ((n + 1)·g2 + 6)(n − 1)/((n − 2)(n − 3)). The forms b1 and b2, reported by MINITAB, use the sample standard deviation. Kurtosis here is excess kurtosis, which is 0 for a normal distribution.
Histogram classes
Sturges’ rule takes ⌈log₂ n⌉ + 1 classes; the Freedman–Diaconis rule uses a width of 2·IQR·n^(−1/3), which resists outliers; Scott’s rule a width of 3.49·s·n^(−1/3); the square-root and Rice rules take ⌈√n⌉ and ⌈2·∛n⌉ classes. By default the width is rounded up to a round number (1, 2, 2.5 or 5 times a power of 10) and the classes start at a multiple of it. Each class includes its lower limit and excludes its upper limit, except the last, which includes both.
Limitations
- Up to 1,000,000 values; the stem-and-leaf plot is drawn for up to 1,000 of them.
- Commas separate values unless you choose decimal commas, so do not type thousands separators: 1,250 is read as 1 and 250, and the tool warns when a value looks like that. In an uploaded file each cell is one value, so 1,250 there is read as 1250.
- A value in brackets, such as (7), is read as −7, the way spreadsheets read accounting negatives.
- It needs the individual values: statistics of grouped data given only as class intervals with frequencies are not computed.
- From an uploaded spreadsheet only the first sheet is read, and formulas are read as their saved values.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
Should I use the sample or the population standard deviation?
If your numbers are the whole group you care about (every student in one class), use the population SD σ. If they are a sample used to describe a larger group, use the sample SD s, which divides by n − 1 to correct the underestimate. For 2, 4, 4, 4, 5, 5, 7, 9, σ = 2 and s ≈ 2.1381.
Why are my quartiles different from my calculator or Excel?
There are several standard ways to compute quartiles. For 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49, Excel’s QUARTILE.INC gives Q1 = 25.5, while the median-of-halves rule of a TI-84 and Excel’s QUARTILE.EXC give 15. Choose the matching method in the tool; the median is the same in every method.
How are outliers found?
With Tukey’s fences: a value below Q1 − 1.5·IQR or above Q3 + 1.5·IQR is an outlier, and one beyond Q1 − 3·IQR or Q3 + 3·IQR is an extreme outlier. For the numbers 1 to 9 and 100, Q1 = 3.25, Q3 = 7.75 and IQR = 4.5, so anything above 14.5 is an outlier and 100 is extreme.
What does the skewness value mean?
Positive skewness means a longer tail to the right (a few large values), negative skewness a longer tail to the left, and a value near 0 a roughly symmetric shape. The adjusted G1 is what Excel’s SKEW returns: for 3, 4, 5, 2, 3, 4, 5, 6, 4, 7 it is 0.3595.
How many histogram classes should I use?
Sturges’ rule, the default, suits moderate, roughly bell-shaped data; Freedman–Diaconis is better for large samples or data with outliers, because it is based on the IQR. For a textbook frequency table, choose “My own class width” and set, for example, a width of 10 starting at 0.
Can I upload a spreadsheet?
Yes — CSV, TSV, TXT, Excel and OpenDocument files (the first sheet). The tool finds the columns that contain numbers and lets you pick one; empty and non-numeric cells are skipped and counted. The file is read in your browser and never uploaded.