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IQR Calculator

Enter the values, and the tool will readily calculate their statistical interquartile range, with the steps shown

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An online interquartile range (IQR) calculator helps you quickly determine how data is distributed by dividing it into quartiles. The tool calculates:

Q1 (first 25% of values)
Q2 (median, 25%–50%)
Q3 (75% percentile)
Q4 (highest 25% of values)

Let’s explore how to use an IQR calculator and understand its statistical relevance step by step. First, we’ll define what an interquartile range is.

What is the Interquartile Range (IQR)?

The interquartile range is a measure of the spread of the middle 50% of a dataset. It shows how tightly or widely the central values are distributed. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). Alternative terms include:

Midspread
Middle 50%
H-spread

If you only need to find the quartiles, a simple quartile calculator can compute Q1, Q2, and Q3 instantly.

IQR Formula:

The formula used is:

IQR = Q3 - Q1

Where:

Q3 = Third quartile (75th percentile)

Q1 = First quartile (25th percentile)

You can also use a mean, median, mode, and range calculator to find other statistical measures or an average calculator for the mean.

How to Use an IQR Calculator:

Follow these steps to calculate the IQR using the online tool. The calculator provides more than just Q1, Q2, and Q3—it also shows other important statistics.

Inputs: Choose how your numbers are separated (comma, space, etc.), then:

Enter the dataset in the input box
Click the calculate button

Outputs: The calculator displays:

IQR value
Q1, Q2, Q3
Mean (average)
Geometric mean
Total sum
Population standard deviation
Sample standard deviation
Range
Number of values
Box plot/IQR graph

Step-by-Step Calculation of IQR

The IQR is calculated using:

IQR = Q3 - Q1

Example: Find the IQR for the dataset 4, 8, 15, 16, 23, 42.

Step 1:

Sort in ascending order: 4, 8, 15, 16, 23, 42

Step 2:

Median (Q2) = average of middle two: (15 + 16)/2 = 15.5

Step 3:

Divide the data into lower half and upper half:

Lower half: 4, 8, 15 → Q1 = 8

Upper half: 16, 23, 42 → Q3 = 23

Step 4:

Apply formula:

IQR = Q3 - Q1 = 23 - 8 = 15

Even Number of Data Points:

Example: 5, 7, 12, 14, 18, 20

Step 1: Sort: 5, 7, 12, 14, 18, 20

Step 2: Median (Q2) = (12 + 14)/2 = 13

Step 3: Lower half: 5, 7, 12 → Q1 = 7

Upper half: 14, 18, 20 → Q3 = 18

Step 4: IQR = Q3 - Q1 = 18 - 7 = 11

FAQs:

How is IQR calculated?

Subtract the first quartile from the third quartile: IQR = Q3 - Q1.

What does IQR indicate?

IQR shows the spread of the middle 50% of data and identifies how closely values cluster around the center.

What is the 1.5 IQR rule?

Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered outliers.

Does a box plot show IQR?

Yes, the box spans Q1 to Q3, visually representing the IQR.

What is quartile deviation?

Quartile deviation = (Q3 - Q1) / 2. It measures half the spread of the middle 50%.

Why is IQR important?

IQR is robust against outliers and gives a clearer picture of typical variability in data.

How to calculate IQR in Excel?

Use =QUARTILE(range,1) for Q1 and =QUARTILE(range,3) for Q3, then subtract Q1 from Q3.

Conclusion:

An online IQR calculator saves time, ensures accuracy, and is especially helpful for students and data analysts to understand data dispersion.

References:

Wikipedia: Interquartile range. Sciencing: Calculating IQR. Scribbr: Methods for IQR.

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