# Quartile Calculator – IQR Calculator

Find the first, second, and third quartiles and the interquartile range of a data set by entering the numbers in the calculator below.

## Results:

First Quartile (Q_{1}): | |
---|---|

Second Quartile (Q_{2}): | |

Third Quartile (Q_{3}): | |

Interquartile Range (IQR): | |

Min: | |

Max: | |

Range: |

## On this page:

## How to Find Quartiles

In statistics, *quartiles* mark the boundaries or divisions of a data set into four equally sized groups.

Given a set of ordered data, when it is split up into four equal groups, the quartiles are the three values that separate each of the groups.

The *first quartile* is also called the lower quartile and is denoted Q_{1}. It represents the 25th percentile, so 25% of the data will be below the first quartile, and 75% will be above it.

The *second quartile* is actually the median of the data, and it’s denoted Q_{2}. The median is a quartile marking the division that separates the upper and lower halves of the data. It represents the 50th percentile, so 50% of the data will be below this quartile.

The *third quartile* is also called the upper quartile and is denoted Q_{3}. It represents the 75th percentile, so 75% of the data will be below it, and 25% will be above it.

- Q
_{1}– first quartile – 25th percentile of the data - Q
_{2}– second quartile – 50th percentile of the data - Q
_{3}– third quartile – 75th percentile of the data

You can find the quartiles by following a few simple steps.

### Step One: Sort the Data

When calculating quartiles, it is essential that you’re working with ordered data, so the first step is to sort the data set from smallest to largest. You can use our ordering numbers calculator to speed this step up.

### Step Two: Find the Median

The second step to finding the quartiles is to find the median. As we noted above, the median is also the second quartile.

The median is the number that is exactly in the middle of the data set. If the data contains an even amount of numbers, then the median is actually the mean of the middle two numbers.

### Step Three: Split the Data into Halves

Next, split the data set into two halves, separated by the median. The numbers below the median will be the first half, and the numbers above the median will be the second.

### Step Four: Find the Quartiles

Now it’s time to find the quartiles.

The first quartile is the median value of the first half of the data. You can find it just like finding the median.

The third quartile is the median value of the second half of the data.

**For example,** let’s find the quartiles of the data [4,8,5,5,7,3,9]

Let’s start by sorting the numbers from smallest to largest. The sorted data should look like this:

[3,4,5,5,7,8,9]

Then, let’s find the median. Recall that the median is the number exactly in the middle.

[3,4,5,5,7,8,9]

Next, split the data into two halves on either side of the median. The two halves should look like this:

[3,4,5] & [7,8,9]

And finally, let’s find the quartiles. Recall that the quartiles are the numbers in the middle of each of the halves of the data.

[3,4,5] & [7,8,9]

So, the quartiles in this data set are:

Q_{1} = 4

Q_{2} = 5

Q_{3} = 8

## How to Find the Interquartile Range

The interquartile range, or *IQR*, is the difference between the first and third quartiles. The interquartile range and quartiles are often used to find outliers in the data.

Finding the interquartile range is very similar to finding the range of the data. The only difference is that the first and third quartiles are used rather than the min and max values.

To find the interquartile range, use the formula:

IQR = Q_{3} – Q_{1}

Where:

IQR = interquartile range

Q_{1} = first quartile

Q_{3} = third quartile

Thus, the interquartile range *IQR* is equal to the third quartile *Q _{3}* minus the first quartile

*Q*.

_{1}