Quartiles and box plots
Cut ordered data into four equal parts, find Q₁ and Q₃, mark the five numbers of a box plot and measure the middle half with the interquartile range.
- UK: Year 10
- France: grade 9
- Germany: grade 7
- Iran: grade 10
- Afghanistan: grade 10
- Syria: grade 9
- Russia: grade 7
Guide
The median cuts ordered data in two halves. The quartiles cut it into four parts with about the same number of values: Q₁ (the lower quartile) has a quarter of the values below it, Q₂ is the median, and Q₃ (the upper quartile) has a quarter above it.
Method: put the data in order and find the median. Q₁ is the median of the lower half and Q₃ is the median of the upper half. When there is an odd number of values the median itself is left out of both halves.
A box plot is drawn from five numbers: the smallest value, Q₁, the median, Q₃ and the largest value. The box holds the middle half of the data, and its length Q₃ − Q₁ is the interquartile range.