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What is the interquartile range of the data set: 5, 6, 7, 8, 9, 10, 11?
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Answer
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Step 1:I'll solve this step-by-step using the precise LaTeX formatting guidelines:
Step 2:: Order the data set from least to greatest
\{5, 6, 7, 8, 9, 10, 11\}
(Note: This data set is already in order)
Step 3:: Find the median (Q2)
Q_{2} = 8
The median is the middle value in the ordered set.
Step 4:: Divide the data set into lower and upper halves
Lower half: $$\{5, 6, 7\}
Upper half: \{9, 10, 11\}
Step 5:: Calculate Q^1 (first quartile)
Q_{1} = 6
Q^1 is the median of the lower half.
Step 6:: Calculate Q^3 (third quartile)
Q_{3} = 10
Q^3 is the median of the upper half.
Step 7:: Calculate Interquartile Range (IQR)
\text{IQR} = Q_{3} - Q_{1} = 10 - 6 = 4
Final Answer
The interquartile range is 4.
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