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How to Use Worksheets On Interquartile Range to Teach Statistics

Statistics is a branch of mathematics that deals with collecting, organizing, analyzing, and interpreting data. One of the topics that students often encounter in statistics is the interquartile range (IQR), which is a measure of how spread out the middle 50% of the data is. The IQR is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3), where Q1 is the median of the lower half of the data and Q3 is the median of the upper half of the data.

Worksheets on interquartile range are a great way to help students practice finding and interpreting the IQR of different data sets. Worksheets can provide students with step-by-step instructions, examples, and exercises that reinforce their understanding of the concept and its applications. Worksheets can also help students compare data sets using the IQR and other measures of central tendency and variability, such as the mean, median, mode, range, and standard deviation.

In this article, we will show you some examples of worksheets on interquartile range that you can use in your classroom or at home. These worksheets are based on Edexcel, AQA, and OCR exam questions, and cover various levels of difficulty. We will also explain how to find the IQR using a simple formula or a box plot, and how to use the IQR to identify outliers and describe data distributions.

Example 1: Finding the IQR from a List of Numbers

The simplest way to find the IQR of a data set is to follow these steps:

• Arrange the data in ascending order (from smallest to largest).

• Find the median (Q2) of the data by locating the middle value or the average of the middle two values.

• Divide the data into two halves: the lower half below Q2 and the upper half above Q2.

• Find Q1 by finding the median of the lower half of the data.

• Find Q3 by finding the median of the upper half of the data.

• Subtract Q1 from Q3 to get the IQR.

For example, consider this worksheet on finding the IQR from a list of numbers:

The solution is as follows:

• The data in ascending order is: 2, 4, 5, 6, 7, 8, 9, 10, 11, 12

• The median (Q2) is (6 + 7) / 2 = 6.5

• The lower half is: 2, 4, 5, 6 and the upper half is: 7, 8, 9, 10, 11, 12

• The lower quartile (Q1) is (4 + 5) / 2 = 4.5

• The upper quartile (Q3) is (9 + 10) / 2 = 9.5

• The interquartile range (IQR) is Q3 - Q1 = 9.5 - 4.5 = 5

Example 2: Finding the IQR from a Frequency Table

If the data is given in a frequency table, we need to first find the cumulative frequency for each class interval. The cumulative frequency is the total number of values that are less than or equal to

the upper limit of each class interval. Then we can use these steps to find

the IQR:

• Find n/4 and 3n/4 where n is

the total frequency.

• Locate n/4 and

3n/4 on

the cumulative frequency axis.

• Draw horizontal lines from n/4 and

3n/4 until they meet

the cumulative frequency curve.

• Draw vertical lines from these points until they 51082c0ec5