Question

the sizes of cans on a shelf are as follows.
18 oz, 8 oz, 16 oz, 20 oz, 20 oz, 16 oz, 12 oz, 8 oz
what is the interquartile range of this list?

Explanation:

Step1: Sort the data

Sort the list of can sizes: \(8,8,12,16,16,18,20,20\)

Step2: Find the median

Since there are \(n = 8\) data points, the median is the average of the \(4^{th}\) and \(5^{th}\) values. The median \(Q_2=\frac{16 + 16}{2}=16\)

Step3: Find \(Q_1\) and \(Q_3\)

The lower half of the data is \(8,8,12,16\). The median of the lower half (\(Q_1\)) is the average of the \(2^{nd}\) and \(3^{rd}\) values. \(Q_1=\frac{8+12}{2} = 10\)
The upper half of the data is \(16,18,20,20\). The median of the upper half (\(Q_3\)) is the average of the \(2^{nd}\) and \(3^{rd}\) values. \(Q_3=\frac{18 + 20}{2}=19\)

Step4: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\)
Substitute \(Q_1 = 10\) and \(Q_3=19\) into the formula: \(IQR=19 - 10=9\)

Answer:

\(9\)