Interquartile range: what it means and how to read it
In the report: iqr — q3 − q1.
How to read it
The width of the middle half of the answers — a spread that ignores extreme values. A common rule marks values more than 1.5 · iqr beyond the quartiles as outliers.
In plain words
A teacher wanted to know how spread out the usual marks of her class were, without a few odd marks spoiling the answer. A quarter of the class got less than 55, q1, and a quarter got more than 85, q3. The iqr came out 30: the middle half of the marks fit into a stretch of 30 points. If the lowest student had got 5 instead of 40, this number would not change at all. A common rule calls a mark odd when it lies more than 45 points past the edges of the middle half, so under 10 or over 130. Now she knows which marks to look at twice.
How it is computed
iqr = q3 − q1Example
The cell with iqr is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — Quartiles and percentiles as in SPSS
=STATS_DESCRIPTIVE(Data!A1:T51, "q1,median,q3,iqr,percentile.12.5", "x,x1")
Where you see it
STATS_DESCRIPTIVE— Column-wise descriptive statistics with flexible metric selection and optional column filtering.
Related values
- Percentile — The q-th percentile, q from 0 to 100, fractions allowed (percentile.12.5); computed as in SPSS, like the quartiles. percentile.0.95 is the 0.95th percentile, not the 95th. Without q or with q outside 0…100 the cell is empty and the error is listed under the table.
- Median absolute deviation — The median of the absolute deviations from the median, without the 1.4826 factor.
- Geometric mean — The n-th root of the product of the values; zero and tiny values are raised to epsilon (Settings), a negative value gives an empty cell.
- Harmonic mean — n divided by the sum of 1/x; zero and tiny values are raised to epsilon (Settings), a negative value gives an empty cell.
- Flatness — The geometric mean of the values as they are divided by their arithmetic mean, without epsilon: a zero among the values gives exactly 0; empty when the mean is 0 or a value is negative.
Get it in your sheet
One formula in a cell gives the whole report, Interquartile range included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)