Question

for exercises 6 - 8, use the box plots to answer the questions. the box plots show the number of points scored by two different teams in their winning games. 6. what are the similarities and differences in the spreads of the two data sets? 7. the two teams are scheduled to play against each other. which team do you think will win? explain. 8. error analysis sheng claims that team b must have played and won more games because the whiskers of the box plot for team b are longer than the whiskers of the box plot for team a. how do you respond to sheng?

Explanation:

Step1: Analyze spread - definition

The spread of a box - plot can be measured by the inter - quartile range (IQR) and the range. The range is the difference between the maximum and minimum values, and the IQR is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$).

Step2: Analyze Team A's spread

For Team A, assume the minimum value is around 18, $Q_1\approx22$, $Q_3\approx28$, and the maximum is around 32. The range is $32 - 18=14$, and the IQR is $28 - 22 = 6$.

Step3: Analyze Team B's spread

For Team B, assume the minimum value is around 10, $Q_1\approx20$, $Q_3\approx26$, and the maximum is around 34. The range is $34 - 10 = 24$, and the IQR is $26 - 20=6$.

Step4: Compare spreads

Similarity: The IQRs of both teams are equal (both 6), which means the middle 50% of the data for both teams have the same spread. Difference: The range of Team B (24) is larger than the range of Team A (14), indicating that the overall spread of Team B's data is greater.

Step5: Predict winning team

There is no clear - cut answer for which team will win. While Team B has a wider overall spread of scores, Team A has higher median and third - quartile values. Team A generally scores more points in the middle 50% of its winning games. However, sports outcomes are unpredictable, and past performance (as shown by the box - plots) is not a definite indicator of future results.

Step6: Error analysis

Sheng's claim is incorrect. The length of the whiskers in a box - plot does not represent the number of games played. The whiskers represent the range of the data excluding outliers (in a simple box - plot interpretation). A longer whisker only means that there is a greater difference between the quartile value and the extreme value in that part of the data set, not the number of games played.

Answer:

1. Similarity: The inter - quartile ranges (IQRs) of both teams are equal (6). Difference: The range of Team B (24) is larger than the range of Team A (14).
2. It's hard to determine which team will win. Team A has a higher median and third - quartile in winning games, but sports results are unpredictable.
3. Sheng's claim is incorrect. The length of the whiskers does not represent the number of games played; it represents the spread of data values outside the middle 50% of the data.