Find the IQR of the following data: 2, 4, 5, 8, 10, 11, 12, 14, 17, 18, 21, 22, 25Give your answer as a number only.
Question
Find the IQR of the following data: 2, 4, 5, 8, 10, 11, 12, 14, 17, 18, 21, 22, 25Give your answer as a number only.
Solution
To find the Interquartile Range (IQR) of a data set, you need to follow these steps:
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Arrange the data in increasing order: 2, 4, 5, 8, 10, 11, 12, 14, 17, 18, 21, 22, 25
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Find the median (Q2) of the data set. Since there are 13 numbers, the median is the 7th number, which is 12.
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Find the lower quartile (Q1), which is the median of the lower half of the data (not including Q2). The lower half of the data is: 2, 4, 5, 8, 10, 11. The median of this data is the average of the 3rd and 4th numbers, which is (5+8)/2 = 6.5.
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Find the upper quartile (Q3), which is the median of the upper half of the data (not including Q2). The upper half of the data is: 14, 17, 18, 21, 22, 25. The median of this data is the average of the 3rd and 4th numbers, which is (18+21)/2 = 19.5.
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Subtract Q1 from Q3 to find the IQR: 19.5 - 6.5 = 13.
So, the IQR of the data set is 13.
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