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Chapter 2: Problem 40

Go to espn.go.com/mlb/teams and select a (or your favorite) team. Click Roster and then Salary. Copy the salary figures for the players into a software program and create a histogram. Describe the shape of the distribution for salary and comment on its center by quoting appropriate statistics.

Short Answer

Expert verified
Create a histogram of the salary data; describe its shape and analyze the mean, median, and mode for central tendency.

Step by step solution

01

Access the Team's Salary Data

Navigate to espn.go.com/mlb/teams. Choose your favorite team and click on 'Roster'. Then click on 'Salary' to view the player's salary data. You should see a list of players with their respective salaries.
02

Collect Salary Data

Copy the salary figures from the webpage. You might need to extract this information manually or use a suitable software extension if available. Make sure you have a complete list of all players' salaries.
03

Input Data into Software

Open a software program capable of data analysis, such as Excel, Google Sheets, or a statistical tool like R or Python. Place all the players' salaries into a single column for simplicity.
04

Create the Histogram

Using the chosen software, generate a histogram. This involves selecting the salary data and instructing the software to create a histogram. The process may differ depending on the software, but typically involves selecting a histogram or chart option.
05

Interpret the Histogram Shape

Observe the shape of the histogram. Determine if it is skewed (left or right), symmetrical, or has any outliers. This observation will give insight into how salary is distributed among players.
06

Calculate and Discuss Central Tendency

Compute the mean (average), median, and mode of the salary data. The mean gives an overall average salary, while the median shows the middle pay, and the mode reveals the most frequent salary. These metrics will help determine the center of the distribution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Histogram creation
Creating a histogram is a straightforward yet powerful way to visualize salary distributions or any set of numerical data.
A histogram is a type of bar chart that groups numerical data into bins or intervals, showing the frequency of data points within each range.
Here鈥檚 how you can create one:
  • First, prepare your data. Ensure that you have a complete list of player salaries from your chosen MLB team.
  • Select data analysis software; options include Excel, Google Sheets, R, or Python's Matplotlib or Seaborn libraries.
  • In the software, input the salary data into a single column for easy analysis.
  • Choose the histogram chart type from the data visualization options.
  • The software will automatically group the salary data into intervals and display the frequency of these intervals as bars in the histogram.
After creating the histogram, pay attention to the shape of the data. This will offer initial insights into the distribution, such as whether salaries are concentrated around a particular range, which leads us to the next concept of understanding the distribution.
Salary distribution analysis
Analyzing salary distribution helps in understanding how salaries vary across players within a team. When observing the histogram created earlier, look for:
  • Skewness: Whether the data tilts towards the right or left. Right-skewed distributions have longer tails on the right, indicating that a small number of players earn significantly more than the rest.
  • Symmetrical Shape: A balanced distribution around the center, suggesting that most player salaries cluster around the average, with few extremes.
  • Outliers: Large salaries stand apart as outliers, affecting the mean and providing insights into the top earners.
By studying the distribution shape, you can tell whether a few high salaries are driving up the average or if there is a general elevation in pay across the board. This analysis is crucial for teams management to understand disparities among salaries and may influence decisions on player contracts and negotiations.
Central tendency measures
Central tendency measures provide a summary statistic that represents the center point or typical value of a dataset. They offer a quick snapshot of the salary data's general trend.
Here are the key measures:
  • Mean: The total salary sum divided by the number of players. It represents the average salary but can be skewed by extreme salaries.
  • Median: The middle value when salaries are sorted from lowest to highest. The median is less affected by outliers and is a better indicator of central tendency in skewed distributions.
  • Mode: The most frequently occurring salary in the dataset. It is valuable in identifying potentially common contract offers or salary caps.
In salary distribution analysis, these measures help summarize the overall financial landscape of a team. By comparing the mean and median, for instance, you can discern the presence of skewness in the data; a large discrepancy often indicates some players earn far more than the median, revealing the financial hierarchy within a team.

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Most popular questions from this chapter

Access the General Social Survey at sda.berkeley. edu/GSS. a. Find the frequency table and histogram for Example 6 on TV watching. (Hint: Enter TVHOURS as the row variable, YEAR(2012) as the selection filter, choose bar chart for Type of Chart, and click Run the Table.) b. Your instructor will have you obtain graphical and numerical summaries for another variable from the GSS. Students will compare results in class.

The workers and the management of a company are having a labor dispute. Explain why the workers might use the median income of all the employees to justify a raise but management might use the mean income to argue that a raise is not needed.

Categorical or quantitative? Identify each of the following variables as categorical or quantitative. a. Number of children in family b. Amount of time in football game before first points scored c. College major (English, history, chemistry,...) d. Type of music (rock, jazz, classical, folk, other)

The owner of a company in downtown Atlanta is concerned about the large use of gasoline by her employees due to urban sprawl, traffic congestion, and the use of energy-inefficient vehicles such as SUVs. She'd like to promote the use of public transportation. She decides to investigate how many miles her employees travel on public transportation during a typical day. The values for her 10 employees (recorded to the closest mile) are \(\begin{array}{llllllllll}0 & 0 & 4 & 0 & 0 & 0 & 10 & 0 & 6 & 0\end{array}\) a. Find and interpret the mean, median, and mode. b. She has just hired an additional employee. He lives in a different city and travels 90 miles a day on public transport. Recompute the mean and median. Describe the effect of this outlier.

Use the empirical rule to explain why the standard deviation of a bell-shaped distribution for a large data set is often roughly related to the range by evaluating Range \(\approx 6 s\). (For small data sets, one may not get any extremely large or small observations, and the range may be smaller, for instance about 4 standard deviations.)
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