Interquartile Range Calculator

Q3 minus Q1 — the spread of the middle half of the data. Unlike the range or standard deviation, it does not change when an outlier gets more extreme.

By Tukey's fences: below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. The 1.5 multiplier is a convention rather than a statistical threshold.

Usually not. An outlier flags a point worth investigating, and it is frequently the most informative observation in the dataset. Removing it because a rule said so discards exactly what was worth understanding.

Points beyond 3 × IQR from the quartiles rather than 1.5. The distinction separates points worth checking from points almost certainly wrong.

Because they are robust. The box shows the middle half, the line shows the median, and the whiskers reach to the fences — none of which moves when an extreme value gets more extreme.

Standard deviation uses every value and its distance from the mean, so one extreme point moves it a great deal. IQR uses only positions, so it does not.

By the same competing methods as percentiles, which is why software packages disagree. The differences are largest on small datasets and vanish on large ones.

A visual summary built on quartiles: a box from Q1 to Q3, a line at the median, whiskers to the fences, and outliers plotted individually. It shows spread and skew at a glance.

It is Tukey's convention, chosen so that roughly 0.7% of normally distributed data falls outside — rare enough to be worth noticing, common enough not to fire constantly.

Yes, and not necessarily removed. An outlier can be a data-entry error, a genuinely unusual case, or the most important observation in the set — and only investigation distinguishes them.

The median of the absolute deviations from the median, an even more robust spread measure than the IQR. It is used where outliers are expected rather than exceptional.

For roughly normal data with no outliers, where it uses all the information rather than only positions. For skewed or contaminated data the IQR is more informative.