Question

select the correct answer from each drop - down menu. the box plot shows the typing speed (in words per minute without errors) of the contestants in a typing contest. team a team b 70 80 90 100 110 120 the interquartile range of team a is, and the interquartile range of team b is. the difference of the medians of team a and team b is. this value is equal to about the interquartile range of either data set.

Explanation:

Step1: Find IQR of team A

Identify $Q_1$ and $Q_3$ from box - plot, calculate $IQR_A=Q_3 - Q_1$.

Step2: Find IQR of team B

Identify $Q_1$ and $Q_3$ from box - plot, calculate $IQR_B=Q_3 - Q_1$.

Step3: Find difference of medians

Identify medians of both teams, calculate $|M_A - M_B|$.

Step4: Relate difference of medians to IQR

Divide difference of medians by IQR.

Answer:

1. For the inter - quartile range of team A:

• First, identify the first quartile ($Q_1$) and third quartile ($Q_3$) from the box - plot of team A. Assume from the box - plot, $Q_1$ of team A is 80 and $Q_3$ is 90.
• The inter - quartile range (IQR) is calculated as $IQR = Q_3 - Q_1$. So, $IQR_A=90 - 80=10$.

1. For the inter - quartile range of team B:

• Assume from the box - plot, $Q_1$ of team B is 85 and $Q_3$ is 95.
• Then $IQR_B = 95 - 85=10$.

1. For the difference of the medians of team A and team B:

• Assume the median of team A ($M_A$) is 85 and the median of team B ($M_B$) is 90.
• The difference of the medians is $|M_A - M_B|=|85 - 90| = 5$.

1. To find how the difference of medians relates to the IQR:

• Since $IQR_A=IQR_B = 10$, and the difference of medians is 5, 5 is about $\frac{1}{2}$ of 10.

So the answers (assuming the above - mentioned values from the box - plot) are:

• The interquartile range of team A is 10.
• The interquartile range of team B is 10.
• The difference of the medians of team A and team B is 5.
• This value is equal to about $\frac{1}{2}$ the interquartile range of either data set.