Data
Spread & quartiles
How spread out is your data? Add points, watch the box plot reshape, and see Q1, median, Q3 and IQR move.
Data
Summary
- Min
- 2
- Max
- 18
- Median
- 8
- Mean
- 8.64
- Q1
- 5.5
- Q3
- 11
- Range
- 16
- IQR
- 5.5
- Std dev
- 4.46
- Count
- 11
Two rivers both average 1 metre deep. One is a steady metre everywhere; the other is ankle-deep at the edges and 3 metres in the middle. The average lies. Spread tells the truth.
Spread (dispersion, variability) measures how scattered data is. The big three: range (crude), interquartile range (robust), and standard deviation (the workhorse).
Risk, consistency, quality control, comparing groups with the same mean — spread is often the more important number than the average.
Both sets have mean 10. Which one is more spread out?
The three spread measures
- Range = max − min. Simplest, but wrecked by one outlier.
- IQR = Q3 − Q1. Robust — ignores the extreme 25% each side.
- Standard deviation = typical distance from the mean. Uses every value; the standard for symmetric data.
- Variance = SD². Same info, but in squared units.
Data: 4, 5, 6, 6, 7, 8, 50. Which spread measure least misled by the 50, and why?
Two investments both return 7% on average. Why prefer the one with lower SD?
Lower SD = less swing = more predictable. High SD means big gains *and* big losses — same average, much bumpier ride. In finance, SD literally *is* 'risk'.
Reporting only the mean is half the story. Always pair a central value with a spread measure — mean ± SD, or median (IQR). A summary without spread can be deeply misleading.
Match the pair: mean goes with standard deviation; median goes with IQR. Don't report a median next to an SD — they assume different things about the data.
- Spread = how scattered the data is — often more telling than the average.
- Range (crude) < IQR (robust) < SD (uses everything).
- Always report a spread measure alongside a central one.