Ask a New Question
Menu

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 and 2
statements 1 and 2

statements 1 and 3
statements 1 and 3

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

statements 2 and 3

1 answer

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

Company A Ages:

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

  1. Mean: \[ \text{Mean} = \frac{\text{sum of ages}}{\text{number of employees}} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = \frac{688}{16} = 43 \]

  2. Median:

    • Order the ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
    • Median (middle value) since there are 16 values (even): \[ \text{Median} = \frac{40 + 41}{2} = 40.5 \]

  3. Range: \[ \text{Range} = \text{maximum} - \text{minimum} = 52 - 27 = 25 \]

Company B Ages:

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

  1. Mean: \[ \text{Mean} = \frac{\text{sum of ages}}{\text{number of employees}} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} = \frac{704}{16} = 44 \]

  2. Median:

    • Order the ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
    • Median (middle values): \[ \text{Median} = \frac{40 + 43}{2} = 41.5 \]

  3. Range: \[ \text{Range} = \text{maximum} - \text{minimum} = 51 - 29 = 22 \]

Summary of Statistics:

  • Company A:

    • Mean: 43
    • Median: 40.5
    • Range: 25

  • Company B:

    • Mean: 44
    • Median: 41.5
    • Range: 22

Evaluating the Statements:

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

    • False (Company A mean = 43, Company B mean = 44)

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

    • True (Company A median = 40.5, Company B median = 41.5)

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

    • True (Company A range = 25, Company B range = 22)

Based on the evaluations:

  • Statements 2 and 3 are true.

The correct response is statements 2 and 3.