Introduction:

The interquartile range (IQR) is a measure of statistical dispersion, which helps in understanding the spread and variability of data. It is particularly useful when working with skewed data sets or when outliers are present. In simpler terms, IQR helps determine where the bulk of values in a dataset lie. In this article, we will learn how to calculate the interquartile range step by step.

Step 1: Arrange the Data

First and foremost, you need to organize your data set in ascending order – meaning sorting it from the smallest to the largest value.

Step 2: Find the Median

Next, identify the median (Q2) value of your data set. The median divides your data set into two equal halves. To find the median:

1. If you have an odd number of data points, simply identify the middle value.

2. If you have an even number of data points, calculate the average of the two middle values.

Step 3: Determine Q1 and Q3

Now that you’ve found the median, you can proceed to find Q1 and Q3 values, which represent the midpoints of both lower half and upper half of your data respectively.

For Q1:

– If you have an odd number of data points in your lower half, identify its median value.

– If there are an even number of data points in your lower half, calculate the average of their two middle values.

Similarly, for Q3:

– If there’s an odd number of data points in your upper half, identify its median value.

– If it’s an even number of data points in your upper half, determine the average of their two middle values.

Step 4: Calculate Interquartile Range (IQR)

Finally, subtract Q1 from Q3 to find out the interquartile range: IQR = Q3 – Q1.

Example:

Let’s calculate the IQR for the following dataset: {5, 8, 12, 15, 18, 22, 25}

1. The dataset is already organized in ascending order.

2. The median (Q2) is 15.

3. The lower half of the data is {5, 8, 12} and the upper half is {18, 22, 25}.

4. Q1 (the median of the lower half) is 8 and Q3 (the median of the upper half) is 22.

5. Therefore, IQR = Q3 – Q1 = 22 – 8 = 14.

Conclusion:

The interquartile range is a crucial measure of statistical dispersion that helps us understand the variability within datasets. By following these simple steps shared in this article, you can easily calculate the interquartile range for any given dataset.