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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 3
statements 1 and 3

statements 1 and 2

:)

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

  1. Mean:

    • Sum of ages: \(34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38 = 705\)
    • Number of employees: \(16\)
    • Mean age: \(705 / 16 = 43.4375 \approx 43.44\)

  2. Median:

    • Sorted ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
    • Since there are 16 values, the median is the average of the 8th and 9th values:
    • Median: \( (40 + 41) / 2 = 40.5\)

  3. Range:

    • Maximum age: \(52\)
    • Minimum age: \(27\)
    • Range: \(52 - 27 = 25\)

Company B

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

  1. Mean:

    • Sum of ages: \(29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48 = 705\)
    • Number of employees: \(16\)
    • Mean age: \(705 / 16 = 43.4375 \approx 43.44\)

  2. Median:

    • Sorted ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
    • Median: \( (43 + 40) / 2 = 41.5\)

  3. Range:

    • Maximum age: \(51\)
    • Minimum age: \(29\)
    • Range: \(51 - 29 = 22\)

Conclusion of Statements:

  1. Mean ages:

    • Company A: ≈ 43.44
    • Company B: ≈ 43.44
    • False: "The mean age of employees from Company A is higher than the mean age of employees from Company B."

  2. Median ages:

    • Company A Median: 40.5
    • Company B Median: 41.5
    • True: "The median age of employees from Company A is lower than the median age of employees from Company B."

  3. Range of ages:

    • Company A Range: 25
    • Company B Range: 22
    • True: "The range of ages of employees from Company A is higher than the range of ages of employees from Company B."

The true statements are 2 and 3. Thus, the correct response is: statements 2 and 3.