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 inter - quartile range definition

The inter - quartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). For a set of data, when the data is ordered from least to greatest, if $n$ is the number of data points, for $n = 6$ (in our case), the first quartile is the median of the lower half of the data and the third quartile is the median of the upper half of the data. The lower half and upper half are divided such that the first quartile is the value at the position $\frac{n + 1}{4}$ (rounded up if necessary) and the third quartile is at the position $\frac{3(n + 1)}{4}$ (rounded up if necessary) in the ordered data - set. For $n=6$, the first quartile is the value at the 2nd position and the third quartile is the value at the 5th position of the ordered data - set.

Step2: Analyze options

The inter - quartile range is the difference between the second and fifth elements of the set after it has been ordered from least to greatest.

Answer:

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