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# Quartile Calculator

Quartile Calculator
Quartile Statistics

First Quartile
Q1 =
Second Quartile
Q2 =
Third Quartile
Q3 =
Interquartile Range
IQR =
Median = Q2
$$\widetilde{x}$$ =
Minimum
Min =
Maximum
Max =
Range
R =

For more detailed statistics use the
Descriptive Statistics Calculator

## Calculator Use

This quartile calculator and interquartile range calculator finds first quartile Q1, second quartile Q2 and third quartile Q3 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 Q1 is the 25th percentile
• The second quartile Q2 is the 50th percentile
• The third quartile Q3 is the 75th percentile

The second quartile Q2 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 Q1 is the median of the lower half not including the value of Q2. The third quartile Q3 is the median of the upper half not including the value of Q2.

## How to Calculate Quartiles

1. Order your data set from lowest to highest values
2. Find the median. This is the second quartile Q2.
3. At Q2 split the ordered data set into two halves.
4. The lower quartile Q1 is the median of the lower half of the data.
5. The upper quartile Q3 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 Q2.

## How to Find Interquartile Range

The interquartile range IQR is the range in values from the first quartile Q1 to the third quartile Q3. Find the IQR by subtracting Q1 from Q3.

• IQR = Q3 - Q1

## 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, x1 ≤ x2 ≤ x3 ≤ ... ≤ xn, the minimum is the smallest value x1. The formula for minimum is:

$\text{Min} = x_1 = \text{min}(x_i)_{i=1}^{n}$

## 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, x1 ≤ x2 ≤ x3 ≤ ... ≤ xn, the maximum is the largest value xn. The formula for maximum is:

$\text{Max} = x_n = \text{max}(x_i)_{i=1}^{n}$

## 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 xn minus x1.

$R = x_n - x_1$

Acceptable Data Formats
Type
Unit
Options
Actual Input Processed
Column (New Lines)
42
54
65
47
59
40
53
42, 54, 65, 47, 59, 40, 53
Comma Separated (CSV)
42,
54,
65,
47,
59,
40,
53,

or

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

or

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

### References

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

Cite this content, page or calculator as:

Furey, Edward "Quartile Calculator | Interquartile Range Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators