A boxplot throws away almost everything and keeps five numbers: the minimum, the three quartiles, and the maximum. From those five it draws a box across the middle half of the data and stretches whiskers out to the edges — but only as far as the data behaves. Anything past the fences is drawn as its own dot. Drag the gold value below and watch the moment it stops being the end of a whisker and becomes a flagged point.
The data and its boxplot
How many points any multiplier would flag
Five numbersdrag the gold point
—
1.5 × IQR
25
Min—
Q1—
Median—
Q3—
Max—
IQR = Q3 − Q1—
Fences—
Flagged—
Send the gold point somewhere — tap to jump
Read the picture back into the five numbers. The left edge of the box is Q1 and the right edge is Q3, so the box covers the middle half of the data and its width is the IQR. The line inside is the median, and it sits wherever it sits — it is not required to be centred, and how far off-centre it sits is your read on skew. The whiskers run out to the most extreme values that are still inside the fences, so a whisker always ends on a real observation, never on the fence itself. Anything beyond gets its own dot. Five numbers, one box, two whiskers: that is the entire object.
Four things people get wrong. A wide section does not hold more data. All four sections hold the same count to within a value or two — carving the data into four same-sized groups is what the quartiles are for, and the live counts under the plot show it every time. So a section twice as wide is not twice as full, it is twice as spread out. A long right whisker means the top quarter is stretched, not crowded. “Outlier” is a flag, not a verdict. The 1.5 is a convention, not a probability: for a bell-shaped population about 0.7% of values land outside the fences by pure chance, so a big sample of perfectly clean data should flag a point or two. Deleting a point because a rule flagged it is how real findings get erased — investigate it instead. Skew alone manufactures flags. Switch to home prices and watch points get flagged with nothing whatsoever wrong; the rule assumes rough symmetry and right-skewed data violates that on the right side by construction. A boxplot cannot show shape. It has no idea whether the middle half is one hump, two humps, or a gap — wildly different datasets can share an identical box.