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QuestionStatistics
Calculate the interquartile range of the data set: {7, 3, 10, 8, 4, 1, 8, 6, 5, 8}
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Answer
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Step 1:: Order the data set from least to greatest.
\text{{1, 3, 4, 5, 6, 7, 8, 8, 8, 10}}
Step 2:: Find the median of the data set.
Since there are 10 numbers, the median is the average of the 5th and 6th numbers.
Step 3:: Remove the median from the data set and find the median of the remaining numbers.
These are the first quartile (Q1) and the third quartile (Q3), respectively. Data set without median: {1, 3, 4, 5, 6} \text{Q^1} = a_{3} = 4 \text{Q^3} = a_{7} = 8
Step 4:: Calculate the interquartile range (IQR) using the formula IQR = Q^3 - Q^1.
\text{IQR} = \text{Q^3} - \text{Q^1} = 8 - 4 = 4
Final Answer
The interquartile range of the data set is 4.
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