# 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.

**Example No. 1**

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

**Example No. 2**

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

2019-03-03

### Comments

Thanks for the quick response.....this is pretty much helpful to the entire world.

Very good article. Information is clearly described. For easy understanding it is very nice to have some examples like there above. Thanks.

### Categories

### New Articles

- Exact values of trigonometric functions
- Signs of trigonometric functions
- Lower and upper quartiles of the data set. Interquartile range
- Mean, mode, median and range of the data set
- Probability of independent events
- Table of basic indefinite functions integrals
- Basic formulas and rules of calculating derivatives
- Removing irrationality from the fractions

## Write a comment