unspurious.calculators

Summarising · One variable

Descriptive Statistics Calculator

Paste a column of numbers and get the full summary — centre, spread, shape and quartiles — with a histogram and box plot, and a note on which average to trust when the data are skewed.

Summary

In plain English

These numbers summarise a single column of data three ways: where it sits, how spread out it is, and what shape it has.

mean
The average — add everything up and divide by how many. Sensitive to extreme values.
median
The middle value once sorted. One huge outlier barely moves it, so it's often the more honest “typical” value.
standard deviation
The typical distance of values from the mean. Bigger = more spread.
quartiles & IQR
Q1 and Q3 mark the 25% and 75% points; the box between them (the IQR) holds the middle half of the data.
skewness
Which way the data lean: positive = a long tail stretching to the right, negative = to the left, near 0 = roughly symmetric.
outlier
A value far from the rest (here, beyond 1.5× the IQR). Worth checking before you trust the mean and SD.

Frequently asked

Which numbers should I trust when my data are skewed?

The median and IQR (interquartile range), rather than the mean and standard deviation. Skew and outliers pull the mean and SD around, while the median and quartiles describe the bulk of the data more honestly.

What counts as an outlier?

A common rule flags any value more than 1.5× the IQR below Q1 or above Q3. Treat it as a prompt to investigate, not a licence to delete — check whether the point is an error or a real (and possibly important) observation.

What do skewness and kurtosis tell me?

Skewness measures lopsidedness — positive means a long right tail, negative a long left tail. Excess kurtosis measures how heavy the tails are relative to a normal distribution. Both describe shape, not centre or spread.

What is the interquartile range, and why use it?

The interquartile range (IQR) is the spread of the middle 50% of the data — the third quartile minus the first (Q3 − Q1). Unlike the range or the standard deviation, it ignores the extreme tails, so a couple of outliers cannot inflate it. That makes it the honest companion to the median for skewed data, and it is exactly what the box of a box plot spans.