Question

team a
team b
which statement is best supported by these data?
a the distributions of the data for team a and team b are approximately symmetrical.
b team b has a greater range in player heights than team a has.
c the mode height of the players on team b is less than the mode height of the players on team a.
d the median height of the players on team b is less than the median height of the players on team a.

Explanation:

Step1: Calculate the range for Team A

The range is the difference between the maximum and minimum values. For Team A, the minimum height is 72 inches and the maximum is 83 inches. So the range for Team A is \(83 - 72=11\) inches.

Step2: Calculate the range for Team B

For Team B, the minimum height is 72 inches and the maximum is 84 inches. So the range for Team B is \(84 - 72 = 12\) inches. Since \(12>11\), Team B has a greater range.

Step3: Check option A

The distribution of Team A is not symmetrical (e.g., the left - hand side has fewer data points compared to the right - hand side in a non - symmetrical way). The distribution of Team B is also not symmetrical.

Step4: Check option C

For Team A, the mode (most frequent value) is 78 inches. For Team B, the mode is 80 inches. So the mode of Team B is greater than that of Team A.

Step5: Check option D

To find the median, first count the number of data points. For Team A, assume there are \(n_A\) data points. Let's count the dots: \(1 + 1+2 + 1+4+3+2+2+2+3=21\) data points. The median is the \(\frac{n + 1}{2}=\frac{21+1}{2}=11^{th}\) data point. Counting the dots (cumulative frequency), the median of Team A is 79 inches. For Team B, count the dots: \(1+1 + 2+1+2+3+5+1+1+2=19\) data points. The median is the \(\frac{19 + 1}{2}=10^{th}\) data point. Counting the dots (cumulative frequency), the median of Team B is 80 inches. So the median of Team B is greater than that of Team A.

Answer:

B. Team B has a greater range in player heights than Team A has.