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

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.

Answer 1

To determine which statement is true based on the provided dot plots for teachers and students, we can analyze the data step by step.

1. Calculate the median number of siblings:

• For teachers, the number of siblings is distributed as follows:

  • 0: 3
  • 1: 3
  • 2: 4
  • 3: 3
  • 4: 2
  • 5: 3
  • 6: 1
  • 9: 1

• The total number of teachers is 20. The median will fall between the 10th and 11th values when organized in ascending order.

• Sorted list: 0 (3), 1 (3), 2 (4), 3 (3), 4 (2), 5 (3), 6 (1), 9 (1) --> 0,0,0,1,1,1,2,2,2,2,3,3,3,4,4,5,5,5,5,6,9.

• The 10th and 11th values are both 2 and 3, so the median for teachers is (2+3)/2 = 2.5.

• For students, the number of siblings is distributed as follows:

  • 0: 1
  • 1: 2
  • 2: 4
  • 3: 5
  • 4: 4
  • 5: 1
  • 6: 2
  • 7: 1

• The total number of students is also 20. Similarly, the median falls between the 10th and 11th values.

• Sorted list: 0 (1), 1 (2), 2 (4), 3 (5), 4 (4), 5 (1), 6 (2), 7 (1) --> 0,1,1,2,2,2,2,3,3,3,3,4,4,5,6,6,6,7,7.

• The 10th and 11th values are both 3, so the median for students is 3.

Thus, the median for students (3) is higher than the median for teachers (2.5).

2. Calculate the maximum number of siblings:

• For teachers, the maximum number of siblings is 9.
• For students, the maximum number of siblings is 7.
• Therefore, the maximum number of siblings for students is not greater than for teachers.

3. Calculate the mean number of siblings:

• The mean for teachers can be calculated based on weighted averages of siblings.
• For students, similarly calculate the mean.

Given that we are requested to evaluate the statements:

1. The first statement is true: "The median number of siblings for students is higher than the median number of siblings for teachers."

Thus, the correct answer is: The median number of siblings for students is higher than the median number of siblings for teachers.