Question

which statement best describes the interquartile range of this set of weights?
{120 lb, 115 lb, 135 lb, 105 lb, 80 lb, 160 lb}
○ the difference between the first and sixth elements of the set as it is written above
● the difference between the second and fifth elements of the set as it is written above
○ the difference between the first and sixth elements of the set after it has been ordered from least to greatest
○ the difference between the second and fifth elements of the set after it has been ordered from least to greatest

Explanation:

Step1: Recall IQR Definition

The interquartile range (IQR) is \( Q_3 - Q_1 \), where \( Q_1 \) (first quartile) is the median of the lower half, and \( Q_3 \) (third quartile) is the median of the upper half. For a set with \( n = 6 \) elements (after ordering), the lower half is the first 3 elements, upper half the last 3. \( Q_1 \) is the 2nd element, \( Q_3 \) is the 5th element (when ordered from least to greatest).

Step2: Analyze Each Option

• Option 1: Difference of first and sixth (original set) is range, not IQR. Eliminate.
• Option 2: Using original set (unordered) for 2nd and 5th is incorrect. IQR requires ordered data. Eliminate.
• Option 3: Difference of first and sixth (ordered) is range (\( \text{max} - \text{min} \)), not IQR. Eliminate.
• Option 4: After ordering, \( Q_1 \) (2nd element) and \( Q_3 \) (5th element) give \( Q_3 - Q_1 \), which is IQR. Correct.

Answer:

the difference between the second and fifth elements of the set after it has been ordered from least to greatest