Question

1. A random sample of 25 of the 400 members of the Bigtime TheaterCompany is surveyed about how many plays each has acted in. Make a boxplot of the data. Then use the box plot to make a qualitative inferenceabout the population. 3, 5, 5, 3, 4, 4, 1, 3, 6, 10, 1, 3, 4, 5, 1, 2, 4, 2, 3, 2, 5,5, 5, 5, 6

Answer 1

1) Let's begin by finding the Quartiles as well as the outliers, with the given data :

`\begin{gathered} 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4,\:4,\:4,\:5,\:5,\:5,\:5,\:5,\:5,\:5,\:6,\:6,\:10 \\ 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4 \\ Median\:of\mathrm{\:}1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4=Q_1=\quad2.5 \\ \\ 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4,\:4,\:4,\:5,\:5,\:5,\:5,\:5,\:5,\:5,\:6,\:6,\:10 \\ Median(Q_2)=4 \\ \\ Q_3 \\ 1,\:1,\:1,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4,\:4,\:4,\:5,\:5,\:5,\:5,\:5,\:5,\:5,\:6,\:6,\:10 \\ 5 \end{gathered}`

Now, that we know the quartiles, let's find the IQR, the interquartile range subtracting from the Upper Quartile the Lower one