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Chapter 3: Problem 87

Explain how the interquartile range is calculated. Give one example.

Short Answer

Expert verified
The interquartile range (IQR) is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). It measures the statistical spread of the data. For a sample dataset 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27, 5 is the Q1 position and Q3 is 18, so, the IQR is 18-5, which equals 13.

Step by step solution

01

Define Interquartile Range

The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). In other words, IQR = Q3 - Q1.
02

Calculate the Quartiles

List the data in numerical order and find the median. The position of the lower quartile (Q1) is found using the formula (n+1) / 4 and the upper (Q3) at 3 * (n+1) / 4, where n is the total number of data points. You might have to interpolate between the numbers in your data set to get the quartiles.
03

Calculate the Interquartile Range

Subtract Q1 from Q3 to calculate the interquartile range. IQR = Q3 - Q1.
04

Example with a sample data

Let's take a sample data: 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27. With n=11, Q1 is the 3rd number (5) and Q3 is the 9th number (18). Therefore, IQR = 18 - 5 = 13.

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