Question

calculate the interquartile range of the skewed dataset 0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10. the interquartile range=□. (1 point) check answer remaining attempts : 3

Explanation:

Step1: Sort the data

The data set is \(0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10\).

Step2: Find the first quartile \(Q_1\)

The formula for the position of \(Q_1\) is \(i=\frac{n + 1}{4}\), where \(n = 15\). So \(i=\frac{15+ 1}{4}=4\). The fourth - value in the sorted data is \(7\), so \(Q_1 = 7\).

Step3: Find the third quartile \(Q_3\)

The formula for the position of \(Q_3\) is \(i=\frac{3(n + 1)}{4}\). Substitute \(n = 15\), we get \(i=\frac{3\times(15 + 1)}{4}=12\). The twelfth - value in the sorted data is \(9\), so \(Q_3=9\).

Step4: Calculate the inter - quartile range (IQR)

The formula for IQR is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 7\) and \(Q_3 = 9\), we get \(IQR=9 - 7=2\).

Answer:

\(2\)