Methodology

This page explains how the calculators on Easy Stat Calc work: the rules they follow, the methods they use, how results are rounded and tested, and the sources behind them. It grows with the site. Each time a new group of calculators goes live, its methods are added here.

Rules every calculator follows

  • The formula is shown. Each calculator page states its formula and works through an example using the calculator’s own output.
  • Conventions are named. When accepted methods differ (sample or population formulas, quartile methods and similar choices), the calculator says which it uses and offers the others as options where they matter.
  • Bad input is reported, not hidden. If an entry cannot be read as a number, it is skipped and named in a note, and results that need more values say how many.
  • Your data stays in your browser. Calculations run on your device. See the Privacy Policy.
  • Nothing goes live untested. See How we test below.

Methods used by the descriptive statistics calculator

This is the calculator on the homepage. All of its results come from one list of numbers.

Averages and position

  • Mean: the sum divided by the count, x̄ = Σx / n.
  • Median: the middle value of the sorted data. With an even number of values it is the average of the two middle values.
  • Mode: the most frequent value. If several values tie, all are shown with how often they appear. If every value appears once, the result is “no mode”.
  • Midrange: (minimum + maximum) / 2.
  • Quartiles: the default is the inclusive method, which matches Excel QUARTILE.INC, Google Sheets and R (type 7). You can switch to the exclusive method, which matches Excel QUARTILE.EXC, or to halves, which matches TI-83 and TI-84 calculators: the median of each half of the data, leaving out the overall median when n is odd.
  • Outliers: values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as possible outliers, using the quartile method you chose.

Spread

  • Range: maximum minus minimum.
  • Sum of squares: SS = Σ(x − x̄)².
  • Variance and standard deviation: both versions are shown. The sample versions divide SS by n − 1 and the population versions divide by n. If you are unsure which you need, use the sample version, which is the usual choice when your data is a sample from a larger group.
  • Standard error of the mean: s / √n.
  • Coefficient of variation: s / |x̄|, shown as a percentage.
  • Mean absolute deviation: Σ|x − x̄| / n, the average distance from the mean.
  • Root mean square: √(Σx² / n).

Shape

Skewness and kurtosis use the same adjusted formulas as Excel SKEW and KURT. Kurtosis is reported as excess kurtosis, so a normal distribution scores 0. Skewness needs at least 3 values and kurtosis at least 4.

Reading your input

Values can be separated by commas, spaces, tabs or line breaks, up to 10,000 values at a time. Use a point for decimals and a minus sign for negative numbers. Anything that is not a number is skipped and listed.

Rounding

Calculations use full precision, and only the displayed answer is rounded: to 4 decimal places by default, or any number from 0 to 10 that you choose. Rounding only at the end avoids the small errors that build up when you round in the middle of a calculation. Computers store numbers with limited precision, so with extremely large or extremely small values the last decimal places can differ slightly from other software.

How we test

  • Every calculator has automatic tests that compare its results with Python’s NumPy and SciPy libraries. They include edge cases such as a single value, identical values, negative numbers, decimals and very large numbers.
  • At least 5 test cases per calculator are also worked out separately in R, Excel or Google Sheets and compared with what the calculator shows, before the page is published.
  • A calculator is not published while any test fails, and its tests are run again after every update.
  • Worked examples on a page are the calculator’s own output, so the page and the tool always agree.

How pages are made

Calculators are coded and tested by Easy Stat Calc. Page text is drafted with AI assistance and reviewed by hand; every formula and example is checked against the calculator.

A page’s “Last updated” date changes only when its content changes, such as a corrected number, a new section or a changed method. Fixing a typo does not change it. Corrections are logged on the Corrections page.

Limits

The calculators use standard textbook methods and are meant for learning, checking work and everyday analysis. For very large data sets, formal publication or specialist analysis, use dedicated software such as R or Python and check your method against your field’s standards.

References

  • NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.11, Measures of skewness and kurtosis. Used for the definitions of skewness and kurtosis. The handbook defines kurtosis so that a normal distribution scores 3; this site reports excess kurtosis (kurtosis minus 3, as Excel does), so a normal distribution scores 0.
  • Illowsky, B. and Dean, S. (2023). Introductory Statistics 2e, section 2.7, Measures of the Spread of the Data. OpenStax, Rice University. Used for sample and population variance and standard deviation.
  • Hyndman, R. J. and Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician, 50(4), 361–365. Used for the quartile methods; the inclusive method matches R’s default (type 7).
  • Joanes, D. N. and Gill, C. A. (1998). Comparing measures of sample skewness and kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 47(1), 183–189. Used for the adjusted sample skewness and kurtosis estimators.
  • Microsoft Excel function documentation: QUARTILE.INC, QUARTILE.EXC, STDEV.S, STDEV.P, SKEW and KURT. Used to describe which Excel function each result matches.
  • NumPy and SciPy documentation, for example scipy.stats.skew. Used as the reference for the automatic tests.

Excel, TI-83, TI-84, Python, R, NumPy and SciPy are trademarks or products of their respective owners. Easy Stat Calc is not affiliated with them. They are named only to show which method a result matches.