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USA Today compared the average graduation rates for male football and basketball scholarship players at top-ranked universities. The graduation rates were expressed as a difference between the graduation rate for scholarship athletes and the university's overall graduation rate for men. A positive number means that the athletes had a graduation rate higher than the overall graduation rate \((+2\) means \(2 \%\) higher) and a negative number means the athletes had a lower graduation rate than the overall graduation rate \((-2\) means \(2 \%\) lower). Using the same scale, construct a dotplot of the graduation rate differences for football players and a dotplot for the graduation rate differences for basketball players. Comment on the similarities and differences in the two plots. $$ \begin{array}{lr} \text { Football } \\ \hline & \begin{array}{l} \text { Difference } \\ \text { from overall } \\ \text { graduation } \end{array} \\ \text { School } & \text { rate } \\ \text { Nebraska } & +8 \\ \text { Kansas State } & +6 \\ \text { Arizona State } & 0 \\ \text { Penn State } & -2 \\ \text { Georgia } & -2 \\ \text { Purdue } & -4 \\ \text { Iowa } & -4 \\ \text { Florida State } & -9 \\ \text { Southern Cal } & -10 \\ \text { Miami } & -11 \\ \text { LSU } & -12 \\ \text { Notre Dame } & -13 \\ \text { Ohio State } & -13 \\ \text { Tennessee } & -13 \\ \text { Virginia } & -14 \\ \text { N.C. State } & -14 \\ \text { Oklahoma } & -14 \\ \text { Auburn } & -19 \\ \text { Virginia Tech } & -20 \\ \text { Colorado } & -21 \\ \text { Wisconsin } & -21 \\ \text { Florida } & -24 \\ \text { Pittsburgh } & -24 \\ \text { Texas } & -26 \\ \text { Michigan } & -35 \\ & \\ \hline \end{array} $$ $$ \begin{array}{lc} \text { Basketball } \\ \hline & \begin{array}{l} \text { Difference } \\ \text { from overall } \\ \text { graduation } \end{array} \\ \text { School } & \text { rate } \\ \text { Butler } & +29 \\ \text { Kansas } & +20 \\ \text { Dayton } & +12 \\ \text { Stanford } & +9 \\ \text { Xavier } & -1 \\ \text { Marquette } & -8 \\ \text { Michigan State } & -10 \\ \text { Creighton } & -17 \\ \text { Florida } & -23 \\ \text { Duke } & -25 \\ \text { Texas } & -26 \\ \text { Arizona } & -27 \\ \text { Illinois } & -29 \\ \text { Wisconsin } & -29 \\ \text { Notre Dame } & -30 \\ \text { Syracuse } & -32 \\ \text { Maryland } & -33 \\ \text { Connecticut } & -38 \\ \text { Wake Forest } & -39 \end{array} $$

Step by step solution

01

Interpret the data

We have two data sets represented in tabular form. Each school represents a data point. A positive number means that the athletes had a higher graduation rate than the overall rate, while a negative number indicates the opposite. The numbers are representing the difference in percentage.

02

Draw the Dotplots

Draw a horizontal line (label it 'Difference from overall graduation rate') for each sport and mark the points corresponding to the differences for each school. Scale should be uniform for both the plots for valid comparison. An easy way to do this is to scale from the smallest to the largest points on the data set. This will result in two dotplots, one for football and basketball.

03

Compare and Comment on the Dotplots

By comparing the location and spread of the two dotplots, observations can be made about the similarities and differences. For example, if many points are concentrated around certain values, this can indicate a trend in the graduation rates for the athletes. This comparison will provide a visual representation of the variation in the difference between the graduate rates of athletes and overall graduates.

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Key Concepts

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

Understanding Data Analysis

Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. In the context of the given exercise, data analysis involves understanding and working with the provided graduation rate differences for scholarship athletes.

The first step in data analysis is to comprehend the data at hand. This involves identifying what a positive or negative number indicates—higher or lower graduation rates compared to the university's overall rate for men. By establishing this context, it becomes easier to interpret the subsequent statistical visualizations.

Importance of Statistical Visualization

Statistical visualization is a critical tool in data analysis, as it helps to represent complex data in a visual format that is easier to understand and interpret. Visualizations can uncover trends, patterns, and outliers that might not be immediately apparent from raw data. In the original exercise, dotplots are used to depict the graduation rate differences.

Comparative Visualization

By creating two dotplots on a uniform scale—one for football and one for basketball—students can make direct comparisons between the two datasets. This visual comparison is more intuitive and can often reveal insights that are not as evident when looking at tables of numbers alone.

Creating and Interpreting Dotplots

Dotplots are a straightforward way to visualize frequency distributions. They are particularly effective when comparing two or more groups, as in the example of graduation rates for different sports. Each dot represents an observation—in this case, a school's graduation rate difference.

Steps in Constructing Dotplots

When creating dotplots, it's essential to maintain a consistent scale and spacing to facilitate accurate visual comparison. Points corresponding to each data value are marked along a horizontal axis. Comparing the dotplots allows us to discern trends such as clustering around certain values or identifying outliers, which in turn may provide insights into the relative academic success of scholarship athletes compared to the overall student body.