Question

ms. barnsley separates her class into two groups. she gives each student the same 25-question math quiz. group a uses a calculator, while group b does not. the table shows the completion times, in minutes, of students in each group.
quiz completion times (minutes)

group a	4.5	4.6	5.0	4.8	4.4	4.7	5.2	4.6	4.8	4.9
group b	5.5	4.0	4.2	4.8	4.1	3.5	3.9	4.3	4.4	4.1

which statement is true about the distributions of completion times?

• the students in group a tended to complete the quiz in less time.
• the median of group a is greater than the median of group b.
• the means of both groups are about the same.
• the standard deviation of group b is less than the standard deviation of group a.

Explanation:

Step1: Analyze Group A's data

First, we sort Group A's completion times: \(4.4, 4.5, 4.6, 4.6, 4.7, 4.8, 4.8, 4.9, 5.0, 5.2\). The median is the average of the 5th and 6th values: \(\frac{4.7 + 4.8}{2} = 4.75\). The mean is \(\frac{4.4 + 4.5 + 4.6 + 4.6 + 4.7 + 4.8 + 4.8 + 4.9 + 5.0 + 5.2}{10} = \frac{47.5}{10} = 4.75\). The data is relatively close together, so the standard deviation is small.

Step2: Analyze Group B's data

Sort Group B's completion times: \(3.5, 3.9, 4.0, 4.1, 4.1, 4.2, 4.3, 4.4, 4.8, 5.5\). The median is the average of the 5th and 6th values: \(\frac{4.1 + 4.2}{2} = 4.15\). The mean is \(\frac{3.5 + 3.9 + 4.0 + 4.1 + 4.1 + 4.2 + 4.3 + 4.4 + 4.8 + 5.5}{10} = \frac{42.8}{10} = 4.28\). The data has a larger spread (from 3.5 to 5.5), so the standard deviation is larger.

Step3: Evaluate each statement

• "The students in Group A tended to complete the quiz in less time": Group A's mean (4.75) and median (4.75) are higher than Group B's mean (4.28) and median (4.15), so this is false.
• "The median of Group A is greater than the median of Group B": Group A's median (4.75) is greater than Group B's median (4.15), so this is true.
• "The means of both groups are about the same": Group A's mean (4.75) and Group B's mean (4.28) are not about the same, so this is false.
• "The standard deviation of Group B is less than the standard deviation of Group A": Group B's data is more spread out, so its standard deviation is larger, not smaller. This is false.

Answer:

The median of Group A is greater than the median of Group B.