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What is the interquartile range of the data set: 5, 6, 7, 8, 9, 10, 11?
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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.