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QuestionStatistics
What is the interquartile range of the data set?
{18,17,10,25,20,20,30,18,18,30,25}
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Answer
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Step 1:
First, we need to find the median of the data set. The data set has 12 numbers, so the median is the 6th number when the data is arranged in order.
Step 2:
Arrange the data in order: {10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30}. The median is 18.
Step 3:
Next, we need to find the first quartile (Q1) and the third quartile (Q3). Q^1 is the median of the lower half of the data set, and Q^3 is the median of the upper half.
Step 4:
The lower half of the data set is {10, 17, 18, 18, 18}, and the median is the 3rd number, which is 18. So, Q^1 = 18.
Step 5:
The upper half of the data set is {20, 20, 25, 25, 30, 30}, and the median is the 4th number, which is 25. So, Q^3 = 25.
Step 6:
The interquartile range (IQR) is the difference between Q^3 and Q^1: IQR = Q^3 - Q^1.
Step 7:
Substitute the values for Q^1 and Q^3: IQR = 25 - 18.
Step 8:
Calculate the result: IQR = 7.
Final Answer
The interquartile range of the data set is 7.
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