Baseball Team Payroll Analysis: Insights from Statistics

1 Leah Mandis BUSN 340 Business Statistics Minor Project 1. Refer to the baseball data in the resources folder in Blackboard. Consider the following variables: 1. Number of wins 2. Payroll 3. Season attendance 4. Whether the team is in the American or National League 5. The number of home runs hit A) Based on the data above, whether the team is in the American or National League is a qualitative variable. On the other hand, the number of wins, the number of home run hits, season attendance, and payroll are all quantitative variables because they are measured numerically. B) Number of wins = Ratio Payroll = Ratio Season attendance = Ratio Whether the team is in the American or National League = Nominal The number of home run hits = Ratio

2 Leah Mandis 2. Refer to the baseball data that reports information on the 30 Major League Baseball teams for the 2010 season. Create a frequency distribution for the team payroll variable and answer the following questions. 32 up to 54 54 up to 76 76 up to 98 98 up to 120 120 up to 142 142 up to 164 164 up to 186 186 up to 208 0 1 2 3 4 5 6 7 8 9 10 Frequency Distribution Chart A) The average payroll for the team is 91.02. I calculated this by averaging the mean of the payroll column in the data set. The minimum value on the payroll is 34.9 and the maximum value is 206.3. The actual range of the data set comes out to 171.4. B) There is some skewness lying in the 186 up to 208 range of the distribution. This shape is the result of a positive skew because the mean is the highest of the three variables (mean = 91.02, median = 84.3, mode = N/A). The team that is within the range that is positively skewing the distribution is the New York Yankees, which makes them the outlier variable.

3 Leah Mandis C) Thirty percent of the teams have a payroll of less than $63,000,000 with the highest of the 30% reaching 62.7 million. Approximately 22 (when rounded) of the teams have a total payroll of less than $100,000,000.00. 3. Find the mean and standard deviation of team payroll for the 14 American League and the 16 National League teams. Does there appear to be a difference in the means? Is there a difference in the dispersion for team payroll between the two leagues? For the 16 National League teams the mean of the payroll is 85.79 and the standard deviation is approximately 33.3. The American League team’s payroll has a mean of about 97 and a standard deviation of 43.7. There is a difference in the payroll means of the two teams. The mean of the AL team was higher because more of the variables were of higher value. The standard deviation for the AL team was also higher because there was more spread in the variables. Type Frequency Cumulative Frequency Cumulative Relative Frequency 32 up to 54 3 3 3/30 = 10% 54 up to 76 9 12 12/30 = 40% 76 up to 98 9 21 21/30 = 70% 98 up to 120 3 24 24/30 = 80% 120 up to 142 3 27 27/30 = 90% 142 up to 164 2 29 29/30 = 96.7% 164 up to 186 0 29 29/30 = 96.7% 186 up to 208 1 30 30/30 = 100%

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4 Leah Mandis 4. Draw a scatter diagram with the variable Wins on the vertical axis and Payroll on the horizontal axis. What are your conclusions? 20 40 60 80 100 120 140 160 180 200 220 0 20 40 60 80 100 120 Wins versus Payroll Payroll Wins After reviewing the scatter diagram and the relationship between the wins and the team’s payroll, I can conclude that there is a positive relationship between the x and y values. As the wins increase the amount the teams are paid also increases. Since the points on the graph are spread out rather than a straight line, I can determine that it is a weak positive correlation between the two variables.

5 Leah Mandis 5. Using the variable Wins, draw a dot plot. What can you conclude from this plot? 50 60 70 80 90 100 0 1 2 3 4 Wins By looking at the dot plot for the variable Wins, I can see that there is not much overlap of the number of wins per team. There are a total of 30 teams represented in this sample. The peaks in this sample are representative of the most common variables in the data set. The data is spread from about 57 to 97 with the highest peak located at 80 wins. I can determine from the shape of this distribution that it is not symmetric. Rather, this dot plot would be considered lightly skewed left since there are less data plots on the left-hand side of the graph. The most common variable of wins on this data set is 80.

Minor Project

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