Question

question: 2. a baseball team scored the following number of runs during their first 10 games: 0, 2, 3, 5, 5, 6, 8, 9, 10, 10. what is the interquartile range for this set of data? a. 5.5 b. 6.0

Explanation:

Step1: Arrange data in ascending order

The data set is \(0,2,3,5,5,6,8,9,10,10\). It is already in ascending - order.

Step2: Find the first quartile \(Q_1\)

The position of \(Q_1\) for \(n = 10\) data points is \(i=\frac{n + 1}{4}=\frac{10+1}{4}=2.75\). So, \(Q_1=2+(3 - 2)\times0.75 = 2.75\).

Step3: Find the third quartile \(Q_3\)

The position of \(Q_3\) is \(i = 3\times\frac{n + 1}{4}=3\times\frac{10 + 1}{4}=8.25\). So, \(Q_3=9+(10 - 9)\times0.25=9.25\).

Step4: Calculate the inter - quartile range (IQR)

\(IQR=Q_3 - Q_1=9.25-2.75 = 6.5\)

Answer:

There is no correct option provided as the calculated inter - quartile range is \(6.5\) and the options are A. \(5.5\) and B. \(6.0\).