11 The distribution of Candiens players salaries is A symmet

11.

The distribution of Candiens players’ salaries is

A.

symmetrical.

B.

slightly right-skewed.

C.

slightly left-skewed.

D.

very right-skewed.

E.

very left-skewed.

12.

The median salary is $______ while the mean is $______.

Answer 1: _____________

Answer 2: ____________

13.

The middle half of players earn between $_____ and $_____, although one star is unusually highly paid at $_____.

Answer 1: _________

Answer 2 : __________

Answer 3: ___________

11.	The distribution of Candiens players’ salaries is
	A. symmetrical. B. slightly right-skewed. C. slightly left-skewed. D. very right-skewed. E. very left-skewed.

Salaries for the 2010-2011 Montreal Canadiens PLAYER SALARY PLAYER SALARY PLAYER SALARY $8,000,000 Andrei Markov $5,000,000 ran Gionta $3,833,000 Andrei Kostitsyn $2,500,000 Hal Gill 1350,000 Josh Gorges 5,500,000 5,000,000 $3,250,000 1,500,000 1,000,000 $875,000 600,000 500,000 $5,750,000 Roman Hamrlik $5,000,000 Tomas Plekanec Scott Gomez Mike Cammalleri Jaroslav Spacek Carey Price Benoit Pouliot Max Pacioretty Yannick Weber David Desharnais 53,250,000 es Wisniewski 53,250,000James Wisniewski mes Wisni1ewski $2,250,000 Travis Moen $1,300,000 Alex Auld $875,000Lars Eller $637,500 Jeff Halpern $550,000Mathieu Darche $875,000 P. K. Subban 600,000 Alexandre Picard Tom Pyatt

Solution

Read the data in R:

data<-read.table(\"http://www.yorku.ca/nuri/econ2500/moorebps6e/data/xrs-2.44-data.txt\",header=T)

attach(data)

names(data)

salary<-data[,2]

sort(salary)

500000 500000 550000 600000 600000 637500 875000 875000 875000 1000000 1300000 1350000 1500000 2250000 2500000 3250000 3250000 3833000 5000000 5000000 5000000 5500000 5750000 8000000

a stem-and-leaf plot of the data, using 100,000s of dollars as the leafs unit, millions for the stems , and dividing each stem into five parts. The distribution is obviously positively skewed and possibly bimodal, and so I decided to make a fivenumber summary of the data

stem(salary,scale=2)

The decimal point is 6 digit(s) to the right of the |

0 | 556666999

1 | 0345

2 | 35

3 | 338

4 |

5 | 00058

6 |

7 |

8 | 0

and the five-number summary is fivenum(salary) 500000 756250 1425000 4416500 8000000

As mentioned, the distribution of salaries is strongly positively skewed, with salaries ranging from halfamillion dollars to 8 million dollars. The median salary is 1.4 million dollars, with half the players earning between 0.8 and 4.4 million. There appear to be two modes: one near the lower end of the distribution, and the other near 5 million dollars. The highest salary, 8 million dollars, appears to be an outlier.