In Exercises 1–3, use the following recent annual salaries (in millions of dollars) for players on the N.Y. Knicks professional basketball team.

23.4 22.5 11.5 7.1 6.0 4.1 3.3 2.8 2.6 1.7 1.6 1.3 0.9 0.9 0.6

NY Knicks Salaries

a. Find Q1 , Q2 , and Q3 .

b. Construct a boxplot.

c. Based on the accompanying normal quantile plot of the salaries, what do you conclude about the sample of salaries?

Salaries (millions of dollars) of basketball team is,

23.4, 22.5, 11.5, 7.1, 6.0, 4.1, 3.3, 2.8, 2.6, 1.7, 1.6, 1.3, 0.9, 0.9, 0.6

a. Sort the given data in ascending order

0.6, 0.9, 0.9, 1.3, 1.6, 1.7, 2.6, 2.8, 3.3, 4.1, 6, 7.1, 11.5, 22.5, 23.4

Total counts of values are 15(n).

The first quantile is given by,

\(\)\(\begin{aligned}{c}{Q_1} = {\left( {\frac{{n + 1}}{4}} \right)^{th\;}}\;term\\ = {\left( {\frac{{15 + 1}}{4}} \right)^{th}}\;term\\ = {4^{th}}\;term\\ = 1.30\end{aligned}\)

The value of \({Q_1} = 1.30\)millions of dollars.

The second quantile is given by,

\(\begin{aligned}{c}{Q_2} = {\left( {\frac{{n + 1}}{2}} \right)^{th\;}}\;term\\ = {\left( {\frac{{15 + 1}}{2}} \right)^{th}}\;term\\ = {8^{th}}\;term\\ = 2.80\end{aligned}\)

The value of \({Q_2} = 2.80\)millions of dollars.

The third quantile is given by,

\(\begin{aligned}{c}{Q_3} = {\left( {\frac{{3\left( {n + 1} \right)}}{4}} \right)^{th\;}}\;term\\ = {\left( {\frac{{3\left( {15 + 1} \right)}}{4}} \right)^{th}}\;term\\ = {12^{th}}\;term\\ = 7.10\end{aligned}\)

The value of \({Q_3} = 7.10\)millions of dollars.

b.

Summary statistics require drawing a box plot.

\(\begin{aligned}{l}Minimum\,value = 0.6\\Maximum\,value = 23.4\end{aligned}\)

\(\begin{aligned}{l}{Q_1} = 1.30\\{Q_2} = 2.80\\{Q_3} = 7.10\end{aligned}\)

Construct the box plot following the given steps:

1. Draw a line with real numbers and mark vertical lines on five values 0.6, 1.3, 2.8, 7.1 and 23.4.
2. Draw a box extending from 1.3 to 7.1, enclosing 2.8.
3. The box plot is shown below:
4. 
   

c) Normality plot describes the normality distribution of the population. The observations in blue are not aligned in a linear pattern. The salaries do not show normality. Hence, the population of these samples does not follow a normal distribution.