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: Sort the data

First, sort the set of weights \(\{120,115,135,105,80,160\}\) from least to greatest.
\(80,105,115,120,135,160\)

Step2: Recall the definition of inter - quartile range

The inter - quartile range (IQR) is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)). For a set of \(n = 6\) data points, the first quartile (\(Q_1\)) is the second element and the third quartile (\(Q_3\)) is the fifth element when the data is ordered.

Step3: Calculate the IQR

\(Q_1=105\), \(Q_3 = 135\)
\(IQR=Q_3 - Q_1\)
\(IQR=135 - 105\)
\(IQR = 30\)

Now, let's check each option:

• Option 1: "the difference between the first and sixth elements of the set as it is written above" \(160 - 80=80\) (incorrect)
• Option 2: "the difference between the second and fifth elements of the set as it is written above" \(135 - 105 = 30\) (correct)
• Option 3: "the difference between the first and sixth elements of the set after it has been ordered from least to greatest" \(160 - 80=80\) (incorrect)
• Option 4: "the difference between the second and fifth elements of the set after it has been ordered from least to greatest" \(135 - 105=30\) but we use the ordered set to identify \(Q_1\) and \(Q_3\) directly, not by re - referencing positions in the ordered set in this non - standard way for IQR.

Answer:

the difference between the second and fifth elements of the set as it is written above