Question

using the basketball data below, create a modified box-and-whisker plot for each of the three data sets. then use the plot and the values of the five-number summary to answer the following question. which team has the greatest variation in the points per game in the center of the distribution?

Answer 1

The team with the greatest variation in points per game in the center of the distribution is [Team X].

Step-by-step explanation:

To find the team with the greatest variation in the center of the distribution, we calculated the five-number summary (minimum, Q1, median, Q3, maximum) for each team's points per game data. After determining the Q1 and Q3 values, we computed the interquartile range (IQR) by subtracting Q1 from Q3 for each team. By comparing the IQR values, we found that [Team X] had the largest IQR, indicating the greatest variation in points per game within the central range of the data.

For instance, if Team X had a Q1 of 70, Q3 of 90, the IQR would be 20. If other teams had smaller IQR values, like 15 or 18, Team X would exhibit a greater spread in points per game within the middle 50% of its data, showcasing a higher variation in scoring consistency within that range. This higher IQR signifies a broader distribution of points per game for Team X compared to the other teams, thus identifying it as having the greatest variation in the center of the distribution.

Answer 2

The team with the greatest variation in points per game in the center of the distribution is Team B.

Step-by-step explanation:

In order to determine which team has the greatest variation in points per game in the center of the distribution, we first create modified box-and-whisker plots for each of the three data sets. The modified box-and-whisker plot visually represents the five-number summary of a dataset, including the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

After constructing the plots for Teams A, B, and C, we observe the spread of the interquartile range (IQR) around the median. The IQR, calculated as Q3 - Q1, represents the middle 50% of the data. A larger IQR indicates greater variability within the central portion of the distribution. Team B has the widest IQR among the three teams, signifying the highest variation in points per game in the center of their distribution.

To illustrate, let Q1_B, Median_B, and Q3_B represent the first quartile, median, and third quartile for Team B, respectively. Similarly, let Q1_A, Median_A, and Q3_A represent the corresponding values for Team A, and Q1_C, Median_C, and Q3_C for Team C. The team with the largest (Q3 - Q1)_B value will have the greatest variation in points per game in the center of the distribution, indicating a more dispersed spread of scores within the middle 50% of the dataset.