Question

Question 1 Use the data below to answer the questions that follow The table below gives the approximate salaries (in millions of dollars) of the 13 members of the Los Angeles Lakers basketball team for the 2011-2012 season. Player Salary Player Salary Kobe Bryant 25.2 millon Derek Fisher Pau Gasol 18.7 millon Matt Barnes 1.9 million Andrew Bynum 15.2 millon Troy Murphy 1.4 million Lamar Odom 8.9 millon Jason Kapone 1.2 million Metta World Peace 6.8 millom Derrick Caracter 0.8 million Luke Walton 5.7 millon Devin Ehanks 0.8 million Steve Blake 4.0 millon The table below gives the approximate salaries (in millions of dollars) for 25 hockey players in Canada for the 2011-2012 con Player Salary Player Salary Player Salary Player Salary Player 1 23.2 millon Player 8 9.3 million Player 15 5.8 millon Player 22 4.3 million Player 2 20.3 millon Player 9 9.1 million Player 16 5.7 millon Player 23 4.0 million Player 3 18.0 millon Player 10 8.7 million Player 17 5.6 millon Player 24 3.6 million Player 4 15.4 millon Player 11 8.4 million Player 18 5.6 millon Player 25 3.3 million Player 5 13.7 millon Player 12 6.4 million Player 19 5.2 millon Player 26 28 million Player 6 10 millon Player 13 6.4 million Player 20 5.2 millon Player 27 1.7 million Player 79.4 millon Player 14 6.3 million Player 21 4.7 millon Player 28 0.9 million (a) (5 points) Fill in the following 2 x 2 contingency table so that it contains counts of players of both kinds of sports who earn at least 10 million dollars or less than 10 million dollars. > 10 million < 10 million Total Basketball Players Hockey Players Total (b) (3 points) Using an appropriate measure, determine which kind of team, basketball or hockey, is more likely to have players that earn at least 10 million dollars (e) Use the Los Angeles Lakers table to answer this question. i. 5 points) Sketch a histogram of the salaries using a bin width of 5 million and as the left endpoint of the first bin. ii. (3 points) Describe the distribution of the salaries of the Los Angeles Lakers (d) Use the Los Angeles Lakers table to answer this question i. (5 points) Draw a boxplot of the salary distribution ii. (2 points) Are there outliers in the salary (e) Use the Los Angeles Lakers table to answer this question. 1. (2 points) Calculate the mean salary li. (3 points) Calculate the standard deviation of the salary distribution.

Answer 1

(a) A 2x2 Contingency table for the data given

	>= 10 million	< 10 million	Total
Basketball Player	3	10	13
Hockey Player	6	22	28
Total	9	32	41

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(b) We use proportion as the best measure to determine that whether basketball or hockey players aremore likely to have earn atleast 10 million

P₁ = BASKETBALL PLAYERS = 3/13 =0.2307

P₂ = HOCKEY PLAYERS = 6/28 = 0.2142

From the propotion measure we found that the basketball players are more likely to have paid atleast 10 million

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(c) Using Los Angeles Lakers table

(i) Histogram of the Salaries

8 7 6 Frequency نیا 2 2- 0 0+ 20 5 10 15 Histogram (Frequency Diagram)

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(ii) The data is Right Skewed

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(d)

(i) Box Plot of the salaries

26 24- 22 20- [18- |16 14 12 |10 6 4. 2

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(ii) There are No outliners

Population size: 13 Median: 4 Minimum: 0.8 Maximum: 25.2 First quartile: 1.3 Third quartile: 12.05 Interquartile Range: 10.75 Outliers: none

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(e) Mean Salary = 7.2308 million

x dx = x -4 = x - 7 dx? 25.2 18.7 15.2 8.9 6.8 5.7 4 3.4 1.9 1.4 1.2 0.8 18.2 11.7 8.2 1.9 -0.2 -1.3 -3 -3.6 -5.1 -5.6 -5.8 -6.2 -6.2 331.24 136.89 67.24 3.61 0.04 1.69 9 12.96 26.01 31.36 33.64 38.44 38.44 0.8 Ex=94 (dx) - 3 (Qx)? = 730.56 Mean x = P2 25.2 + 18.7-15.2 -8.9+ 6.8 +5.7-4-3.4 -1.9 -1.4 +1.2 + 0.8 -0.8 13 94 13 = 7.2308 i = 7.2308 is not an integer, use assumed mean method A = 7

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(ii) Standard deviation of salary = 7.4929

Σα. (Σα) ? Population Standard deviation c = n 730.56 - (3) 13 13 730.56 - 0.6923 13 729.8677 13 56.1437 = 7.4929

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