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The ages of randomly selected employees at two companies are recorded. Their ages are as follows.

Company A: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
Company B: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48

Which of the following statements is true?

The mean age of employees from Company A is higher than the mean age of employees from Company B.
The median age of employees from Company A is lower than the median age of employees from Company B.
The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
(1 point)
Responses

statements 1, 2, and 3
statements 1, 2, and 3

statements 2 and 3
statements 2 and 3

statements 1 and 2
statements 1 and 2

statements 1 and 3

1 answer

To evaluate which statements are true, we will calculate the mean, median, and range of ages for both companies.

Company A:

Ages: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38

  1. Mean Age: \[ \text{Mean} = \frac{\text{Sum of ages}}{\text{Number of employees}} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = \frac{ 34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = 40.375 \]

  2. Median Age:

    • Sort the ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
    • The median is the average of the 8th and 9th numbers: \[ \text{Median} = \frac{40 + 41}{2} = 40.5 \]

  3. Range: \[ \text{Range} = \text{Max age} - \text{Min age} = 52 - 27 = 25 \]

Company B:

Ages: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48

  1. Mean Age: \[ \text{Mean} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} = \frac{776}{16} = 48.5 \]

  2. Median Age:

    • Sort the ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
    • The median is the average of the 8th and 9th numbers: \[ \text{Median} = \frac{43 + 43}{2} = 43 \]

  3. Range: \[ \text{Range} = \text{Max age} - \text{Min age} = 51 - 29 = 22 \]

Now compare the statements:

  1. The mean age of employees from Company A is higher than the mean age of employees from Company B.

    • Company A mean = 40.375, Company B mean = 40.5: False

  2. The median age of employees from Company A is lower than the median age of employees from Company B.

    • Company A median = 40.5, Company B median = 43: True

  3. The range of ages of employees from Company A is higher than the range of ages of employees from Company B.

    • Company A range = 25, Company B range = 22: True

Conclusion:

The true statements are 2 and 3.

The correct option is: statements 2 and 3.