# Quartile Calculator

## Calculator Use

This quartile calculator and interquartile range calculator finds first quartile Q_{1}, second quartile Q_{2} and third quartile Q_{3} of a data set. It also finds median, minimum, maximum, and interquartile range.

Enter data separated by commas or spaces.

You can also copy and paste lines of data from spreadsheets or text documents. See all allowable formats in the table below.

## Quartiles

Quartiles mark each 25% of a set of data:

- The first quartile Q
_{1}is the 25th percentile - The second quartile Q
_{2}is the 50th percentile - The third quartile Q
_{3}is the 75th percentile

The second quartile Q_{2} is easy to find. It is the median of any data set and it divides an ordered data set into upper and lower halves.

The first quartile Q_{1} is the median of the lower half not including the value of Q_{2}. The third quartile Q_{3} is the median of the upper half not including the value of Q_{2}.

## How to Calculate Quartiles

- Order your data set from lowest to highest values
- Find the median. This is the second quartile Q
_{2}. - At Q
_{2}split the ordered data set into two halves. - The lower quartile Q
_{1}is the median of the lower half of the data. - The upper quartile Q
_{3}is the median of the upper half of the data.

If the size of the data set is odd, do not include the median when finding the first and third quartiles.

If the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q_{2}.

## How to Find Interquartile Range

The interquartile range IQR is the range in values from the first quartile Q_{1} to the third quartile Q_{3}. Find the IQR by subtracting Q_{1} from Q_{3}.

- IQR = Q
_{3}- Q_{1}

## How to Find the Minimum

The minimum is the smallest value in a sample data set.

Ordering a data set from lowest to highest value,
*x _{1} ≤ x_{2} ≤ x_{3} ≤ ... ≤ x_{n}*, the minimum is the smallest value

*x*. The formula for minimum is:

_{1}## How to Find the Maximum

The maximum is the largest value in a sample data set.

Ordering a data set from lowest to highest value,
*x _{1} ≤ x_{2} ≤ x_{3} ≤ ... ≤ x_{n}*, the maximum is the largest value

*x*. The formula for maximum is:

_{n}## How to Find the Range of a Set of Data

The range of a data set is the difference between the minimum and maximum. To find the range, calculate x_{n} minus x_{1}.

Unit

Options

54

65

47

59

40

53

54,

65,

47,

59,

40,

53,

or

42, 54, 65, 47, 59, 40, 53

65 47

59 40

53

or

42 54 65 47 59 40 53

54 65,,, 47,,59,

40 53

### References

[1] Wikipedia contributors. "Quartile." Wikipedia, The Free Encyclopedia. Last visited 10 April, 2020.