The dot plot below shows the ages of students at a summer soccer camp. Each X represents one student.

Question

The dot plot titled Ages of students at a summer soccer camp has age from 9 to 13 on the horizontal line. There are 1 X above 9, 2 X’s above 10, 3 X’s above 11, 2 X’s above 12, and 1 X above 13.

Which of the following statements is true regarding this data? Select all that apply.
A.
The distribution of the ages has a bell shape.


B.
There is a peak at 4.


C.
The mean age is 11.


D.
The median age is 11.


E.
There were 11 students at the camp.


F.
The oldest student at the camp was 11 year

Answer 1

To analyze the dot plot you've described, let's summarize the data first:

• Ages and corresponding number of students:
  • Age 9: 1 student
  • Age 10: 2 students
  • Age 11: 3 students
  • Age 12: 2 students
  • Age 13: 1 student

Now, let's evaluate the statements:

A. The distribution of the ages has a bell shape.

• False. A bell-shaped distribution typically refers to a normal distribution. This data appears to have a peak around age 11 but does not exhibit the symmetrical properties that characterize a bell shape.

B. There is a peak at 4.

• False. The highest peak is at age 11 (with 3 students), not at age 4.

C. The mean age is 11.

• False. To find the mean, calculate the total ages: (19 + 210 + 311 + 212 + 1*13) / 9 = (9 + 20 + 33 + 24 + 13) / 9 = 109 / 9 ≈ 12.11.

D. The median age is 11.

• True. To find the median, you can list the ages: 9, 10, 10, 11, 11, 11, 12, 12, 13. The middle value (5th number in the sorted list) is indeed 11.

E. There were 11 students at the camp.

• True. By adding the number of X’s: 1 + 2 + 3 + 2 + 1 = 9 students total.

F. The oldest student at the camp was 11 years.

• False. The oldest student was 13 years old (1 student).

Based on this analysis, the true statements regarding the data are:

• D. The median age is 11.
• E. There were 11 students at the camp.