The interquartile range (IQR) is a useful statistical measure that represents the dispersion or spread of data. It quantifies the range containing the middle 50% of a dataset by calculating the difference between the lower quartile (Q1) and upper quartile (Q3). The IQR is an insightful tool in identifying outliers and understanding the distribution of data. In this article, we will discuss how to calculate the IQR step by step.

1. Arrange the data in ascending order

Before starting any calculation, ensure that your dataset is sorted in ascending order, from the smallest to the largest value.

2. Find the median

The median is the middle value of a dataset when arranged in ascending order. It can be easily found by locating the middle number or taking an average of two center values for even-numbered datasets. The median effectively splits your data into two halves.

3. Determine Q1 and Q3

Q1 or First Quartile is essentially the median of the lower half of data points, excluding the overall median obtained previously if it falls within your dataset. Similarly, Q3 or Third Quartile is calculated as the median of the upper half of data points while ignoring the overall median if applicable.

4. Calculate IQR

Now that we have Q1 and Q3 values, we can determine IQR with a simple subtraction: IQR = Q3 – Q1. The resulting value represents 50% spread around any given dataset’s central tendency, making it robust against influences from extreme values or outliers.

For better understanding, let’s work through an example:

Suppose we have a dataset: 2, 5, 8, 9, 12, 18, 22

1. Ascending Order: Our dataset is already sorted in ascending order.

2. Median: As there are an odd number of data points, the median is ‘9’.

Lower half: 2, 5, 8

Upper half: 12, 18, 22

3. Q1 and Q3 Calculation:

Q1 (median for lower half) = 5

Q3 (median for upper half) = 18

4. IQR Calculation:

IQR = Q3 – Q1 = 18 – 5 = 13

In conclusion, the interquartile range for our dataset is approximately 13 units. This simple calculation will help you make informed decisions about your data distribution, potential outliers, and overall trends.