1) Create a frequency distribution for the Team Salary variable and answer the questions: 4 points.
The frequency distribution for the team salary variable was as shown in figure 1.
Figure 1
2) What is the range of Salary? 2 points
The range is given by:
= maximum value – minimum value
= 223.35 – 69.06 = 154.29
The range is 154.29.
3) What is the shape of the distribution? Does it appear that any of the teams have a salary that is out of line with the others? 4 points
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The distribution appears to be left-skewed or negatively skewed as it features a long tail on the left. The salaries that are above 200 appear to be out of line with the others.
4) Draw a cumulative relative frequency distribution of team salary. Using this distribution, forty percent of the teams have a salary of less than what amount? 4 points.
Table 1.
| X-Values | Frequency | Cumulative Frequency |
| 61-80 | 4 | 4 |
| 81-100 | 8 | 12 |
| 101-120 | 7 | 19 |
| 121-140 | 3 | 22 |
| 141-160 | 2 | 24 |
| 161-180 | 3 | 27 |
| 181-200 | 1 | 28 |
| 201-220 | 1 | 29 |
| 221-240 | 1 | 30 |
| Total | 30 |
Figure 2
From the calculation, 40% of 30 = 12. From the cumulative distribution, the 12th payroll features earnings of $100 million. Forty percent of the teams thus have a salary of less than $100 million.
The first 12 payrolls in order are 69.06, 70.76, 73.65, 80.28, 84.64, 85.89, 86.34, 87.62, 98.26, 98.68, 98.71, and 99.63. From the given analysis, 12 of the teams have a payroll of less than $100 million with the twelfth team earning $99.63 million.
5) About how many teams have a total salary of more than $220 million? 4 points
1 team has a total salary of more than $220 million.
PART II TASKS
1) The Year Opened is the first year of operation for that stadium. For each team, use this variable to create a new variable, stadium age, by subtracting the value of the variable Year Opened from the current year. 2 points
The new variable stadium age was calculated as show in the excel column tab labeled “Stadium age”.
2) Develop a box plot with the new variable Stadium Age. 4 points
The variables that were used to create the box plot were as shown:
58, 11, 108, 20, 20, 12, 54, 26, 16, 16, 21, 14, 17, 106, 28, 47, 31, 10, 11, 29, 19, 25, 24, 26, 19, 8, 54, 30, 22, 20.
Figure 3
Box Plot for stadium age variables
3) Are there any outliers? If so, which of the stadiums are outliers? 4 points
The outliers are the variables 54, 54, 58, 106, and 108.
4) Using the variable salary create a box plot. Are there any outliers? 4 points
The variables that were used to create the box plot were as shown:
70.76, 87.62, 115.59, 182.16, 116.65, 98.71, 116.73, 86.34, 98.26, 172.28, 69.06, 112.91, 146.45, 223.35, 84.64, 98.68, 108.26, 99.63, 213.47, 80.28, 133.05, 85.89, 126.37, 166.50, 122.71, 120.30, 73.65, 144.31, 112.90, 166.01
Figure 4
Box plot for team salary values.
There are no outliers.
5) Compute the Salary quartiles using formula 4-1. Write a brief summary of your analysis 4 points.
The quartiles to be computed are Q1, Q3, and the interquartile range (IQR)
The Formula for Q1 = ¼ (n + 1) th term
The Formula for Q3 = ¾ (n + 1) th term
The Formula for Q2 = Q3 – Q1
Q1 = ¼ (30+1) = 7.75 th term
Q1 = 7 th + 0.75(8 th – 7 th ) observation
Q1 = 86.34 + 0.75 (87.62-86.34)
Q1 = 87.3
Q3 = ¾ (30+1) = 23.25 th term
Q3 = 23 rd + 0.25(24 th – 23 rd ) observation
Q3 = 144.31 + 0.25 (146.45 - 144.31)
Q3 = 144.845
IQR = 57.545
Outliers 1.5*IQR = 86.3175
The first quartile was 87.3, the third quartile was 144.845 and the interquartile range was 57.545.
Values above (86.3175 + 144.845) = 231.1625 and below (87.3 - 86.3175) = 0.9825 are outliers. There are no values above this range indicating that there are no outliers.
The IQR of 57.545 also indicates that the spread of the variables ‘Team Salary’ is even and small indicating that the mean is a representative of the data. The small spread also indicates that there are no large differences between the variables.
6) Draw a scatter diagram with the variable Wins on the vertical axis and salary on the horizontal axis. What are your conclusions? 4 points.
Figure
From the scatterplot, there is a positive correlation between the variables. An increase in the team’s salary could thus lead to an increase in the number of wins. However, the relationship between the variables appears to be rather weak. The weak relationship was caused by some variables that had several wins but did have a high team salary.
