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: Calculate mean of Group A

Sum Group A values: $4.5+4.6+5.0+4.8+4.4+4.7+5.2+4.6+4.8+4.9 = 47.5$
Mean: $\frac{47.5}{10} = 4.75$

Step2: Calculate mean of Group B

Sum Group B values: $5.5+4.0+4.2+4.8+4.1+3.5+3.9+4.3+4.4+4.1 = 42.8$
Mean: $\frac{42.8}{10} = 4.28$

Step3: Find median of Group A

Sort Group A: $4.4, 4.5, 4.6, 4.6, 4.7, 4.8, 4.8, 4.9, 5.0, 5.2$
Median: $\frac{4.7+4.8}{2} = 4.75$

Step4: Find median of Group B

Sort Group B: $3.5, 3.9, 4.0, 4.1, 4.1, 4.2, 4.3, 4.4, 4.8, 5.5$
Median: $\frac{4.1+4.2}{2} = 4.15$

Step5: Assess standard deviation trend

Group A values cluster tightly around 4.5-5.2; Group B has wider spread (3.5 to 5.5). So Group B has larger standard deviation.

Step6: Evaluate each option

1. Group A mean (4.75) > Group B mean (4.28): False.
2. Group A median (4.75) > Group B median (4.15): True.
3. Means (4.75 vs 4.28) are not similar: False.
4. Group B std dev > Group A: False.

Answer:

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