Home · Probability and statistics · Lower and upper quartiles of the data set. Interquartile range

# Lower and upper quartiles of the data set. Interquartile range

Quartiles of the data set are the values that divide a list of numbers into quarters.

Calculations are very simple. Firstly put the list of numbers in order. Then divide your list into four equal parts. The quartiles are at the places of divisions. If places of divisions are between numbers, then we should find mean of two nearest numbers. Q1 is lower quartile, Q2 is middle quartile and Q3 is upper quartile.
Interquartile range is the difference between upper Q3 and lower Q1 quartiles.

## Solved examples

Find the quartiles of this data set: 9, 7, 3, 2, 1, 2, 5.

First of all, we put the list of numbers in order: 1, 2, 2, 3, 5, 7, 9. Then we cut the list of numbers into four equal parts: $$\require{enclose} 1, \enclose{verticalstrike}{2}, 2, \enclose{verticalstrike}{3}, 5, \enclose{verticalstrike}{7}, 9$$ Quartile 1 (Q1) = 2
Quartile 2 (Q2) = 3
Quartile 3 (Q3) = 7

Here we have a data set: 3, 5, 3, 4, 7, 8, 2, 3, 8, 2, 1, 5. Find lower and upper quartiles of this data set. Then calculate an interquartile range.

First of all, we put the list of numbers in order: 1, 2, 2, 3, 3, 3, 4, 5, 5, 7, 8, 8. Then we cut the list of numbers into four equal parts: $$1,2,2,|\ 3,3,3,|\ 4,5,5,|\ 7,8,8$$ Lower quartile (Q1) = (2 + 3)/2 = 2.5
Upper quartile (Q3) = (5 + 7)/2 = 6
Interquartile Range (Q3 - Q1) = 6 - 2.5 = 3.5