Question

The table shows the number of shutouts that ten baseball pitchers had in their careers. A shutout is a complete game pitched without allowing a run. $$\begin{array}{|I|l|c|c|}\hline \text { Pitcher } & \text { Shutouts } \\\\\hline \text { Warren Spahn } & \text { 63 } \\\\\hline \text { Christy Mathewson } & 80 \\\\\hline \text { Eddie Plank } & 69 \\\\\hline \text { Nolan Ryan } & 61 \\\\\hline \text { Bert Blyleven } & 60 \\\\\hline \text { Don Sutton } & 58 \\\\\hline \text { Grover Alexander } & 90 \\\\\hline \text { Walter Johnson } & 110 \\\\\hline \text { Cy Young } & 76 \\\\\hline \text { Tom Seaver } & 61 \\\\\hline\end{array}$$ What number could you add to the set of data to make it have more than one mode? Explain why you chose the number.

Short answer

Any number could be added. For example, by adding 63 to the dataset, both 63 (Warren Spahn) and the newly added 63 will occur twice, making them modes of the dataset. This will result in a bimodal data set.

Step-by-step solution

Determine the Frequency of Data Points

Count the number of times each value appears in the dataset. As all the shutout numbers are unique, they all have a frequency of 1 in the dataset.

Identify Potential Modes

Decide on the number that could become a mode. Since the aim is to have more than one mode, choose a value that is not already a mode. Any number from the dataset can be selected as this exercise does not specify certain conditions for the number.

Add the Chosen Number to the Data

Introduce the chosen number to the dataset. This creates a bimodal dataset since this number now appears twice in the dataset.