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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 2 and 3
statements 2 and 3

statements 1 and 3
statements 1 and 3

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

statements 1 and 2
statements 1 and 2
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1 answer

To determine which statements are true, we need to calculate the mean, median, and range of the ages for both companies.

Company A: Ages

  • Ages: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
  • Mean: \[ \text{Mean} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = \frac{ 680 }{16} = 42.5 \]
  • Median: Sort the values: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
    • There are 16 values (even), so the median is the average of the 8th and 9th values: \[ \text{Median} = \frac{40 + 41}{2} = 40.5 \]
  • Range: \[ \text{Range} = 52 - 27 = 25 \]

Company B: Ages

  • Ages: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
  • Mean: \[ \text{Mean} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} = \frac{ 608 }{16} = 38 \]
  • Median: Sort the values: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
    • There are 16 values (even), so the median is the average of the 8th and 9th values: \[ \text{Median} = \frac{43 + 43}{2} = 43 \]
  • Range: \[ \text{Range} = 51 - 29 = 22 \]

Now, let's evaluate each statement:

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

    • Company A mean = 42.5, Company B mean = 38
    • True

  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:

All statements are true. Therefore, the correct answer is: statements 1, 2, and 3.