This Quartile calculator and interquartile range calculator determines the first quartile (Q1), second quartile (Q2), and third quartile (Q3) for a data set. It also calculates the median, minimum, maximum, and interquartile range.

Enter your data using commas or spaces. You can also copy and paste data lines directly from spreadsheets or text documents. See the table below for all supported formats.

How to Use the Interquartile Range Calculator

Example 1

Sample question: Find the interquartile range for this set of numbers: 1, 2, 4, 5, 7, 9, 10, 14, 17.

1. Enter your numbers in the text box. Commas are optional, so you can separate the values with spaces instead. If commas are omitted, the calculator will add them automatically.
2. Click the “Find the Interquartile Range!” button.
3. Scroll down to view the results. The calculator displays the interquartile range, along with the 1st quartile (25th percentile), 2nd quartile (50th percentile or median), and 3rd quartile (75th percentile). This also helps when using a Median interquartile range calculator.

For this data set, the results are:

• 25th Percentile: 3
• 50th Percentile: 7
• 75th Percentile: 12
• Interquartile Range: 9

Tip: If you want to work out the result manually or understand How to calculate Q1 and Q3, use the formula IQR = Q3 − Q1:

9.5 − 3 = 6.5

Example 2

Sample question: Find the interquartile range for the following data set: 12, 13, 15, 18, 19, 22, 88, 89, 90, 91, 92, 93, 95, 98, 99, 101, 101, 103, 105, 106, 107, 108, 109, 200, 201, 201, 203, 204, 215, 216, 217, 222, 223, 224, 225, 227, 229, 230, 232, 245, 246, 250, 258, 270, 271, 271, 272, 273.

1. Enter your data in the Data Set box. Separate each value with commas. With a large data set, copying and pasting the numbers can be faster. For this example, enter the complete comma-separated data directly into the Data Set: box.
2. Click the “Find the Interquartile Range!” button. The interquartile range appears in bold at the bottom of the results.

Results

• 25th Percentile: 94
• 50th Percentile: 200.5
• 75th Percentile: 228
• Interquartile Range: 134

Tip: The interquartile range equation is IQR = Q3 − Q1. If you need to show your working, use the values from the results list in the equation:

75th percentile 200.5 for Q1
25th percentile 228 for Q2

IQR = Q3 − Q1 = 200.5 − 94 = 134

The same process can be used to find the Interquartile range of 10 numbers or another data set by entering the values into the calculator.

What Is Interquartile Range?

The interquartile range (IQR) is a statistical measure of dispersion that shows how widely the middle 50% of a data set is spread. It is found by subtracting the lower quartile (Q1) from the upper quartile (Q3), as demonstrated in various Interquartile range examples.

A smaller IQR means the middle half of the values are grouped more closely together, while a larger IQR indicates greater spread among those values. This makes the IQR useful for understanding the central portion of a data set.

Unlike the range, which can be strongly influenced by unusually small or large values, the IQR is less affected by outliers. This is also why an Interquartile range calculator grouped data approach can be useful when working with data arranged into groups.

Interquartile Range Formula

The interquartile range is calculated using the formula IQR = Q3 − Q1.

Here, Q1 represents the lower quartile, while Q3 represents the upper quartile. The IQR shows the distance between these two quartile values.

This calculator is designed to determine the IQR when you already know how to calculate Q1 and Q3. If you need help finding either quartile manually, a quartile calculator can provide a useful way to work them out.

How to Find the Interquartile Range

You can work out the interquartile range manually in three stages:

1. Determine the lower quartile, Q1.
2. Determine the upper quartile, Q3.
3. Use the interquartile range formula to find the difference between them.

Example

Find the interquartile range for this data set: 8, 10, 12, 14, 18, 20, 22, 24.

Step 1: Determine Q1

Arrange the values from smallest to largest, then find the median of the lower half. For this data set, the first quartile is Q1 = 11.

Step 2: Determine Q3

Next, find the median of the upper half of the ordered data. Here, the third quartile is Q3 = 21.

Step 3: Use the IQR formula

The formula is:

IQR = Q3 − Q1

Substitute the values:

IQR = 21 − 11

IQR = 10

You can also check the result with the IQR calculator by copying the data set into the input field and selecting calculate. The calculator will provide the corresponding result and show how the value was obtained.

Therefore, IQR = 10, meaning the middle 50% of the data set covers a spread of 10 units.

Calculation Steps

1. Arrange the data values in ascending order, from the smallest to the largest.
2. Find Q1 (25th percentile), which is the value below which 25% of the data falls.
3. Find Q2, or the median (50th percentile), which represents the middle value of the data set.
4. Find Q3 (75th percentile), the value below which 75% of the data falls.
5. Calculate the interquartile range using IQR = Q3 − Q1.

Outlier Detection

The interquartile range can help identify potential outliers using the 1.5 × IQR rule. This method establishes lower and upper boundaries based on Q1, Q3, and the IQR.

Lower Fence = Q1 − 1.5 × IQR

Upper Fence = Q3 + 1.5 × IQR

Any data value below the lower fence or above the upper fence is treated as an outlier under this rule.

Five-Number Summary

A five-number summary gives a compact view of how the values in a data set are distributed. It includes five key points:

• Minimum: The smallest value in the data set.
• Q1: The first quartile, or 25th percentile.
• Median (Q2): The middle value, or 50th percentile.
• Q3: The third quartile, or 75th percentile.
• Maximum: The largest value in the data set.

These five values form the basis of a box plot, also known as a box-and-whisker plot.

IQR vs Range

The range and interquartile range both measure how much a data set varies, but they focus on different portions of the values. The range is calculated by subtracting the minimum from the maximum, while the IQR is found by subtracting Q1 from Q3.

The range represents the total spread across the entire data set. In contrast, the IQR shows how widely the middle 50% of the values are distributed.

A key difference is their response to outliers. Because the range uses the minimum and maximum values, extreme observations can have a strong effect on it. The IQR is less influenced by unusually high or low values because it concentrates on the middle half of the data.

When to Use IQR

The interquartile range is useful in several situations where you need to understand the spread of data without giving too much weight to extreme values:

• Skewed distributions: When data is not normally distributed, the IQR can provide a clearer measure of spread than standard deviation.
• Data with outliers: Because extreme values have less influence on the IQR, it can be more robust than the range or standard deviation.
• Outlier detection: The IQR can be used to identify potential outliers systematically.
• Box plots: The IQR determines the size of the box in a box-and-whisker plot.
• Comparing groups: IQRs can help compare the spread of different groups without allowing extreme values to dominate the comparison.

Percentile Methods

The calculator provides two standard approaches for calculating percentiles:

• Inclusive (default): This method corresponds to Excel’s PERCENTILE.INC and R type 7. It uses linear interpolation between data points and is suitable for most applications.
• Exclusive: This approach corresponds to Excel’s PERCENTILE.EXC and R type 6. It leaves the minimum and maximum values outside the interpolation range and can be more conservative when detecting outliers.

Quartile Calculator/Quartile Finder

The interquartile range calculator also works as a quartile calculator, allowing you to find the first and third quartiles for any numerical data set along with the interquartile range.

1. Enter your data in the Data Set box.
2. Click “Find the Interquartile Range.”
3. Review the results provided by the calculator.
4. In the results, the 25th percentile represents the first quartile (Q1), while the 75th percentile represents the third quartile (Q3).

FAQs

Conclusion

The interquartile range calculator makes it easier to find Q1, Q2, Q3, the median, and IQR while also helping with outlier detection and data spread. Whether you are checking a small data set or working with larger values, the calculator provides a practical way to verify your calculations.

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