Question

1. the box - plots show the number of points scored in each game between two rival football teams. of the statements given check all that are true.

the pandas have a larger range of scores.
the zebras scored between 10 and 20 points more often than they scored 25 - 20 points.
the zebras have a smaller median than the pandas.
in 50% of the pandas games the team scored between 21 and 40 points.

Explanation:

Step1: Recall box - plot properties

A box - plot shows the five - number summary: minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum. The inter - quartile range (IQR) is $Q_3 - Q_1$, and the range is $max - min$.

Step2: Analyze the Zebra's box - plot

For the Zebra's box - plot, assume the minimum is around 10, $Q_1$ is around 20, median is around 25, $Q_3$ is around 30, and maximum is around 45.

Step3: Analyze the Panda's box - plot

For the Panda's box - plot, assume the minimum is around 20, $Q_1$ is around 25, median is around 35, $Q_3$ is around 40, and maximum is around 55.

Step4: Check the first statement

The range for Zebras is $45 - 10=35$, and for Pandas is $55 - 20 = 35$. So, the statement "The Panda's have a larger range of scores" is False.

Step5: Check the second statement

The Zebra's median is around 25 and the Panda's median is around 35. So, the statement "The Zebra's have a smaller median than the Panda's" is True.

Step6: Check the third statement

For Zebras, the IQR is $30 - 20 = 10$. The proportion of data between $Q_1$ and $Q_3$ is 50%. The number of games where Zebras scored between 10 and 20 points is less than 50% of the games. For Pandas, 50% of the data is between $Q_1 = 25$ and $Q_3=40$. So, the statement "In 50% of the Panda's games the team scored between 21 and 40 points" is True.

Step7: Check the fourth statement

We cannot say that Zebras scored between 25 - 30 points more often than they scored between 10 - 20 points just from the box - plot. Box - plots do not show frequency within intervals in that detail. So, the statement "The Zebra's scored between 25 - 30 points more often than they scored between 10 - 20 points" is False.

Answer:

• The Zebra's have a smaller median than the Panda's.
• In 50% of the Panda's games the team scored between 21 and 40 points.