How to Find Interquartile Range of a Data Set
In statistics, the interquartile range (IQR) is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles. It is a useful measure of the spread of a dataset, particularly when outliers are present. In this article, we will guide you through the process of finding the interquartile range of a data set, step by step.
Step 1: Arrange the Data in Order
The first step in finding the interquartile range is to arrange the data in ascending order. This will help you identify the quartiles more easily. For example, if you have the following data set:
10, 15, 20, 25, 30, 35, 40, 45, 50
You would arrange it as follows:
10, 15, 20, 25, 30, 35, 40, 45, 50
Step 2: Find the Median
The median is the middle value of the data set. If the data set has an odd number of observations, the median is the middle number. If the data set has an even number of observations, the median is the average of the two middle numbers. In our example, the data set has 9 observations, so the median is the 5th number:
10, 15, 20, 25, 30, 35, 40, 45, 50
The median is 30.
Step 3: Split the Data into Two Halves
Now, split the data into two halves. The lower half contains the numbers below the median, and the upper half contains the numbers above the median. In our example:
Lower half: 10, 15, 20, 25
Upper half: 35, 40, 45, 50
Step 4: Find the First Quartile (Q1)
The first quartile (Q1) is the median of the lower half. In our example, the lower half has 4 numbers, so we find the median of these 4 numbers:
10, 15, 20, 25
The median is 17.5.
Step 5: Find the Third Quartile (Q3)
The third quartile (Q3) is the median of the upper half. In our example, the upper half has 4 numbers, so we find the median of these 4 numbers:
35, 40, 45, 50
The median is 42.5.
Step 6: Calculate the Interquartile Range (IQR)
Finally, calculate the interquartile range by subtracting the first quartile from the third quartile:
IQR = Q3 – Q1
IQR = 42.5 – 17.5
IQR = 25
So, the interquartile range of our data set is 25.
In conclusion, finding the interquartile range of a data set involves arranging the data in order, finding the median, splitting the data into two halves, and calculating the medians of the lower and upper halves. This measure provides valuable insights into the spread of the data and is an essential tool in statistical analysis.
