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

1 answer

To analyze the given data and statements, let's calculate the mean, median, and range for both companies based on the provided ages.

Company A Ages:

  • Ages: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
  • Sorted Age: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
  • Mean: \[ \text{Mean} = \frac{(34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38)}{16} = \frac{688}{16} = 43 \]
  • Median:
    • Since there are 16 numbers, 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
  • Sorted Age: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
  • Mean: \[ \text{Mean} = \frac{(29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48)}{16} = \frac{689}{16} = 43.0625 \]
  • Median:
    • Since there are 16 numbers, 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 evaluate the statements:

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

    • True: 43 > 43.0625 (incorrect comparison; needs to be 43 < 43.0625)

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

    • True: 40.5 < 43

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

    • True: 25 > 22

Since the analysis shows:

  • The first statement is false,
  • The second statement is true,
  • The third statement is true.

The correct answer is: statements 2 and 3.