Question

consider the groups of numbers in the box below.
group a: 4, 5, 6, 7, 8
group b: 2, 4, 6, 8, 10
which statement about group b is true?
a. group b has a larger mean and a larger standard deviation.
b. group b has a larger mean and a smaller standard deviation.
c. group b has the same mean as group a and a larger standard deviation.
d. group b has the same mean as group a and a smaller standard deviation.

Explanation:

Step1: Calculate mean of Group A

Group A: 4, 5, 6, 7, 8. Mean = $\frac{4 + 5 + 6 + 7 + 8}{5}$ = $\frac{30}{5}$ = 6.

Step2: Calculate mean of Group B

Group B: 2, 4, 6, 8, 10. Mean = $\frac{2 + 4 + 6 + 8 + 10}{5}$ = $\frac{30}{5}$ = 6.

Step3: Analyze standard deviation

Standard deviation measures spread. Group A values: 4,5,6,7,8 (closer to mean 6). Group B values: 2,4,6,8,10 (more spread out from 6). So Group B has same mean as A, larger standard deviation.

Answer:

C. Group B has the same mean as Group A and a larger standard deviation.