Question

read the example. then, choose the best answers.
two groups of students took a science test, and their scores are as follows:
group a: 70, 75, 78, 81, 85
group b: 65, 70, 75, 81, 88
5.11) what is the mode of group as scores?
a. 75
b. 78
c. there are two modes.
d. there is no mode.
5.12) what is the median of group bs scores?
a. 70
b. 75
c. 81
d. 83
5.13) what is the range of group as scores?
a. 10
b. 15
c. 20
d. 25
5.14) which group has the higher mean score, and what is the difference between the means of the two groups?
a. group a, difference is 2
b. group a, difference is 3
c. group b, difference is 2
d. group b, difference is 3
5.15) which two statements are true about the sets of data?
□ group a performed better than group b, with higher mean and median scores.
□ group a scores are more spread out than those in group b.
□ group b has a mode score of 75, which means it is the most common score in that group.
□ group b scores are more spread out than those in group a.
□ group b has a higher median score than that of group a.

Explanation:

Step1: Find mode of Group A

Mode is the most - frequent value. In Group A: 70, 75, 78, 81, 85, each value appears only once. So there is no mode.

Step2: Find median of Group B

Arrange Group B scores 65, 70, 75, 81, 88 in ascending order. Since there are 5 values (odd number), the median is the middle - value, which is 75.

Step3: Find range of Group A

Range = maximum value - minimum value. For Group A, maximum = 85, minimum = 70, so range = 85 - 70=15.

Step4: Find means of Group A and B

Mean of Group A: $\frac{70 + 75+78 + 81+85}{5}=\frac{389}{5}=77.8$. Mean of Group B: $\frac{65 + 70+75 + 81+88}{5}=\frac{379}{5}=75.8$. Group A has a higher mean, and the difference is 77.8 - 75.8 = 2.

Step5: Analyze statements in 5.15

• Mean of Group A (77.8) > Mean of Group B (75.8), median of Group A (78) > median of Group B (75), so Group A performed better.
• Range of Group A (15) < Range of Group B (88 - 65 = 23), so Group B scores are more spread out.
• Group B has no mode as each value appears only once.

Answer:

5.11) D. There is no mode.
5.12) B. 75
5.13) B. 15
5.14) A. Group A, difference is 2
5.15) Group A performed better than Group B, with higher mean and median scores; Group B scores are more spread out than those in Group A.