Use the image to answer the question.

Question

An illustration shows two sets of number lines with dot plots. They are titled teachers and students showing number of siblings in each respectively. The first number line is for teachers with arrows on both the ends. It ranges from 0 to 10 in increments of 1. It shows 3 closed circles over the 0 marking, 3 closed circles over the 1 marking, 4 closed circles over the 2 marking, 3 closed circles over the 3 marking, 2 closed circles over the 4 marking, 3 closed circles over the 5 marking, 1 closed circle over the 6 marking and 1 closed circle over the 9 marking. The second number line is for teachers with arrows on both the ends. It ranges from 0 to 10 in increments of 1. It shows 1 closed circle over the 0 marking, 2 closed circles over the 1 marking, 4 closed circles over the 2 marking, 5 closed circles over the 3 marking, 4 closed circles over the 4 marking, 1 closed circle over the 5 marking, 2 closed circles over the 6 marking and 1 closed circle over the 7 marking.

Twenty students and twenty teachers are randomly selected. They were asked how many siblings they have. The data is shown in the dot plots. Which of the following statements is true?

(1 point)
Responses

The maximum number of siblings for students is greater than the maximum number of siblings for teachers.
The maximum number of siblings for students is greater than the maximum number of siblings for teachers.

The mean number of siblings for teachers is higher than the mean number of siblings for students.
The mean number of siblings for teachers is higher than the mean number of siblings for students.

The range of the number of siblings for teachers is lower than the range of the number of siblings for students.
The range of the number of siblings for teachers is lower than the range of the number of siblings for students.

The median number of siblings for students is higher than the median number of siblings for teachers.

Answer 1

To analyze the statements based on the provided dot plots for teachers and students, we should first determine the relevant statistics: the maximum, mean, range, and median number of siblings.

1. Maximum number of siblings:

   • Teachers: The maximum from the dot plot is 9 (with 1 closed circle).
   • Students: The maximum from the dot plot is 7 (with 1 closed circle).

   So, the maximum number of siblings for students is not greater than that for teachers.

2. Mean number of siblings:

   • Teachers:
     • Calculation:
       • (0×3 + 1×3 + 2×4 + 3×3 + 4×2 + 5×3 + 6×1 + 9×1) / 20
       • = (0 + 3 + 8 + 9 + 8 + 15 + 6 + 9) / 20
       • = 58 / 20 = 2.9
   • Students:
     • Calculation:
       • (0×1 + 1×2 + 2×4 + 3×5 + 4×4 + 5×1 + 6×2 + 7×1) / 20
       • = (0 + 2 + 8 + 15 + 16 + 5 + 12 + 7) / 20
       • = 65 / 20 = 3.25

   Thus, the mean number of siblings for teachers (2.9) is not higher than that for students (3.25).

3. Range of siblings:

   • Teachers: Maximum is 9, minimum is 0; range = 9 - 0 = 9.
   • Students: Maximum is 7, minimum is 0; range = 7 - 0 = 7.

   Therefore, the range of the number of siblings for teachers (9) is indeed higher than that of the students (7).

4. Median number of siblings:

   • Teachers: When sorted, the number of siblings will be:
     • 0 (3), 1 (3), 2 (4), 3 (3), 4 (2), 5 (3), 6 (1), 9 (1)
     • This results in: 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 6, 9
     • The median (10th and 11th values) = (2+3)/2 = 2.5.
   • Students: When sorted, the number of siblings will be:
     • 0 (1), 1 (2), 2 (4), 3 (5), 4 (4), 5 (1), 6 (2), 7 (1)
     • This results in: 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7
     • The median = (3+3)/2 = 3.

   Hence, the median number of siblings for students (3) is indeed higher than that for teachers (2.5).

Based on this analysis, the correct statement is:

The median number of siblings for students is higher than the median number of siblings for teachers.