Question

The amount that two groups of students spent on snacks in one day is shown in the dot plots below.

Group A
A dot plot titled Group A. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.

Group B
A dot plot titled Group B. A number line going from 0 to 5 labeled Amount in Dollars. There are 0 dots above 0, 3 above 1, 2 above 2, 4 above 3, 0 above 4, and 1 above 5.

Which statements about the measures of center are true? Select three choices.
The mean for Group A is less than the mean for Group B.
The median for Group A is less than the median for Group B.
The mode for Group A is less than the mode for Group B.
The median for Group A is 2.
The median for Group B is 3.

Answer 1

1. The mean for Group A is less than the mean for Group B

2. The median for Group A is less than the median for Group B.

3. The mode for Group A is less than the mode for Group B.

Explanation:

1. To find the mean for Group A, you use the formula: Total sum/Total frequency.

To find the total sum, you multiply the frequency(how many times the given number is repeated) with the given numbers.

0 × 0 = 0

1 × 5 = 5

2 × 4 = 8

3 × 1 = 3

4 × 0 = 0

5 × 0 = 0

Total Sum: 5 + 8 + 3 = 16

Total frequency: 5 + 4+ 1 = 10

`(16)/(10)` = 1.6

To find the mean for Group B, you repeat everything above.

0 × 0 = 0

1 × 3 = 3

2 × 2 = 4

3 × 4 = 12

4 × 0 = 0

5 × 1 = 5

Total Sum: 3 + 4 + 12 + 5 = 24

Total frequency: 3 + 2 + 4 + 1 = 10

`(24)/(10)` = 2.4

2. I can't explain it but I'm certain that it is correct.

3. The most repeated number for Group A is 1, it is repeated 5 times, while the most repeated number in Group B is 3, it is repeated 4 times.