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Statistics Unit Test

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Question
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 1 and 2
statements 1 and 2

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

statements 2 and 3

1 answer

To determine the correctness of the statements, let's calculate the mean, median, and range for each company.

Company A Ages

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

  1. Mean: \[ \text{Mean} = \frac{\text{Sum of ages}}{\text{Number of employees}} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} \] \[ = \frac{ 454 }{ 16 } \approx 28.375 \]

  2. Median: First, sort the ages in ascending order: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52

    Since there are 16 data points, the median is the average of the 8th and 9th values: \[ \text{Median} = \frac{ 40 + 41 }{ 2 } = 40.5 \]

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

Company B Ages

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

  1. Mean: \[ \text{Mean} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} = \frac{ 723 }{ 16 } \approx 45.1875 \]

  2. Median: First, sort the ages in ascending order: 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 values: \[ \text{Median} = \frac{43 + 43}{2} = 43 \]

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

Comparison of Means, Medians, and Ranges

  1. Mean: \[ \text{Mean (A)} \approx 40.25 \quad \text{and} \quad \text{Mean (B)} \approx 45.1875 \] Company A's mean is lower than Company B's.

  2. Median: \[ \text{Median (A)} = 40.5 \quad \text{and} \quad \text{Median (B)} = 43 \] Company A's median is lower than Company B's.

  3. Range: \[ \text{Range (A)} = 25 \quad \text{and} \quad \text{Range (B)} = 22 \] Company A's range is higher than Company B's.

Conclusion

  • Statement 1: False (mean A < mean B)
  • Statement 2: True (median A < median B)
  • Statement 3: True (range A > range B)

The correct option is:

  • statements 2 and 3.