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Question
The list shows the number of employees at seven companies.
525, 650, 539, 643, 764, 539, 687
What is the interquartile range of these numbers?
To find the interquartile range, we first need to find the lower quartile (Q1) and the upper quartile (Q3).
Step 1: Arrange the numbers in ascending order:
525, 539, 539, 643, 650, 687, 764
Step 2: Find the median.
The median of the entire data set is the number that lies in the middle when the numbers are arranged in ascending order. In this case, the median is the number that separates the lower half of the data set from the upper half. Since there are 7 numbers, the median is the (7+1)/2 = 4th number, which is 643.
Step 3: Find the lower quartile (Q1).
Q1 is the median of the lower half of the data set. In this case, the lower half is 525, 539, 539. There are 3 numbers, so the median is the (3+1)/2 = 2nd number, which is 539.
Step 4: Find the upper quartile (Q3).
Q3 is the median of the upper half of the data set. The upper half is 650, 687, 764. There are 3 numbers, so the median is the (3+1)/2 = 2nd number, which is 687.
Step 5: Calculate the interquartile range.
The interquartile range is the difference between Q3 and Q1.
Q3 - Q1 = 687 - 539 = 148.
Therefore, the interquartile range of these numbers is 148.