Math Playground

Data

Spread & quartiles

How spread out is your data? Add points, watch the box plot reshape, and see Q1, median, Q3 and IQR move.

05101520Q1 5.5med 8Q3 11

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 data sets can have the same average and look completely different. Spread tells you how scattered the values are around that average.

Spread, four ways

  • Range — biggest minus smallest
  • Quartiles — split sorted data into four equal chunks
  • Interquartile range (IQR) — Q3 minus Q1, the middle 50% spread
  • Standard deviation — typical distance from the mean
Try it

Data: 2, 4, 4, 4, 5, 5, 7, 9. Range?

9 − 2 = 7.

Range is fooled by one weird value. IQR and standard deviation are sturdier — they don't jump just because of one outlier.