What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9, 10}?
Practice Questions
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What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9, 10}?
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Questions & Step-by-Step Solutions
What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9, 10}?
Step 1: Arrange the data set in ascending order. The data set is already arranged: {1, 3, 7, 8, 9, 10}.
Step 2: Find the median of the data set. The median is the average of the two middle numbers (7 and 8) since there are 6 numbers. Median = (7 + 8) / 2 = 7.5.
Step 3: Divide the data set into two halves. The lower half is {1, 3, 7} and the upper half is {8, 9, 10}.
Step 4: Find Q1 (the median of the lower half). The lower half is {1, 3, 7}. The median (Q1) is 3.
Step 5: Find Q3 (the median of the upper half). The upper half is {8, 9, 10}. The median (Q3) is 9.
Step 6: Calculate the interquartile range (IQR) using the formula IQR = Q3 - Q1. IQR = 9 - 3 = 6.
