What this calculator gives you
| Group | Statistics |
|---|---|
| Center | Mean, median, mode, midrange, geometric and harmonic mean |
| Spread | Sample and population standard deviation and variance, range, IQR, mean absolute deviation, coefficient of variation, standard error |
| Position | Minimum, Q1, median, Q3, maximum, any percentile, outlier fences and outliers |
| Shape | Skewness and excess kurtosis, with a plain-English reading |
How to report descriptive statistics
- For roughly symmetric data, report the mean and standard deviation. For the default test scores above: “M = 80.9, SD = 9.35, n = 10”.
- For skewed data or data with outliers, report the median and IQR, e.g. “Mdn = 82.5, IQR = 16”.
- Always include the sample size, and a chart such as a histogram or box plot.
Choosing a quartile method
Software disagrees on quartiles for small data sets. The default here, the median of the lower and upper halves, matches the TI-84 and most school textbooks. Excel’s QUARTILE.INC and Google Sheets use the inclusive method; QUARTILE.EXC, Minitab and SPSS use the exclusive method. With large data sets the differences become tiny.
Need just one statistic with the full working? Try the standard deviation, mean, median and mode or five-number summary calculators.
Worked example: reading the default results
For the ten test scores loaded by default (72, 85, 90, 66, 78, 88, 95, 70, 81, 84):
- Center: mean 80.9, median 82.5. They are close, so the scores are roughly symmetric.
- Spread: standard deviation 9.35 and IQR 16 (Q1 = 72, Q3 = 88). The coefficient of variation is 11.6%, a moderate spread.
- Shape: skewness −0.22, roughly symmetric. Excess kurtosis is −0.94, so the tails are lighter than a normal distribution’s (the scores are spread fairly evenly).
- Precision: the standard error of the mean is 2.96, so with only 10 students the class average is known to within a few points.
Common mistakes to avoid
- Reporting the mean and SD for skewed data. Report the median and IQR too, or instead.
- Over-reading skewness and kurtosis from small samples. With fewer than about 30 values, both can swing widely.
- Forgetting the sample size. Always report n alongside the statistics.
Do it in other software
| Software | How |
|---|---|
| Excel | Data › Data Analysis › Descriptive Statistics (Analysis ToolPak) produces a similar summary table. |
| Python | pandas: df["x"].describe(), plus df["x"].skew() and df["x"].kurt(). |
| R | summary(x), sd(x), and skewness/kurtosis from the moments package. |
| TI-84 | STAT › CALC › 1-Var Stats. |
Related tools: Standard Deviation Calculator, Five-Number Summary Calculator, Histogram Maker, Box Plot Maker and Mean, Median & Mode Calculator.