Descriptive statistics calculator
One paste, the whole summary. Each number links to the page that explains it step by step.
Mean 74.75, median 73.5, SD 10.166. The data look roughly symmetric.
| Statistic | Value | Explained on |
|---|---|---|
| Count n | 20 | steps |
| Sum | 1495 | |
| Mean x̄ | 74.75 | steps |
| Median | 73.5 | steps |
| Mode | none | steps |
| Minimum | 58 | steps |
| Q1 | 68 | steps |
| Q3 | 82 | steps |
| Maximum | 95 | steps |
| Range | 37 | steps |
| IQR | 14 | steps |
| Sample SD s | 10.1664 | steps |
| Population SD σ | 9.909 | steps |
| Sample variance s² | 103.3553 | steps |
| Population variance σ² | 98.1875 | steps |
| Standard error s/√n | 2.2733 | steps |
| Coefficient of variation | 13.6005% | |
| Skewness | 0.2704 | steps |
| Excess kurtosis | −0.4993 | steps |
Reading a descriptive summary
Start with shape, then centre, then spread. The box plot and histogram above show shape at a glance. If the data are roughly symmetric with no outliers, report the mean and standard deviation. If they are skewed or have outliers, report the median and IQR (the five number summary), because those are not dragged by extreme values.
The five number summary
Minimum, Q1, median, Q3 and maximum split the sorted data into four groups of equal size. The quartiles here use Tukey's median-of-halves method, the same as the TI-84; the quartile calculator also shows the interpolated (Excel) values.
Shape statistics
- Skewness is the adjusted Fisher–Pearson coefficient (Excel SKEW). Between −0.5 and 0.5 is usually treated as roughly symmetric.
- Excess kurtosis (Excel KURT) compares tail heaviness with a normal distribution, which scores 0. Positive values mean heavier tails and more extreme values.
- Coefficient of variation is SD ÷ mean as a percentage: a unit-free way to compare spread between data sets on different scales. It is only meaningful for data on a ratio scale with a positive mean.
Your data are shared with the other data tools on this site, so you can jump to the histogram maker or percentile calculator without pasting again.
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Questions students ask
What is a five number summary?
Minimum, first quartile (Q1), median, third quartile (Q3) and maximum. Together they describe the centre, spread and range of a data set and are exactly what a box plot draws.
What are descriptive statistics?
Numbers that summarise a data set without generalising beyond it: measures of centre (mean, median, mode), spread (range, IQR, standard deviation, variance) and shape (skewness, kurtosis). Inferential statistics, like confidence intervals, go further and draw conclusions about a population.
What does skewness tell me?
Skewness measures asymmetry. Near 0 means roughly symmetric; positive means a longer right tail (mean usually above the median); negative means a longer left tail. Values beyond about ±1 indicate strong skew. This page reports the adjusted Fisher–Pearson sample skewness, the same as Excel SKEW().
What is the standard error of the mean?
SE = s / √n, the typical distance between a sample mean and the true population mean. It shrinks as the sample grows and is the building block of confidence intervals.