To determine which statements are true, we will calculate the mean, median, and range of ages for both companies.
Company A: Ages: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
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Mean: \[ \text{Mean} = \frac{\text{Sum of ages}}{\text{Number of ages}} \] \[ \text{Sum of ages} = 34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38 = 684 \] \[ \text{Mean} = \frac{684}{16} = 42.75 \]
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Median:
- First, sort the ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
- Since there are 16 numbers, the median is the average of the 8th and 9th values: \[ \text{Median} = \frac{40 + 41}{2} = 40.5 \]
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Range: \[ \text{Range} = \text{Maximum age} - \text{Minimum age} = 52 - 27 = 25 \]
Company B: Ages: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
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Mean: \[ \text{Sum of ages} = 29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48 = 708 \] \[ \text{Mean} = \frac{708}{16} = 44.25 \]
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Median:
- First, sort the ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
- Since there are 16 numbers, the median is the average of the 8th and 9th values: \[ \text{Median} = \frac{43 + 43}{2} = 43 \]
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Range: \[ \text{Range} = \text{Maximum age} - \text{Minimum age} = 51 - 29 = 22 \]
Summary of Results:
- Mean (Company A: 42.75, Company B: 44.25)
- Median (Company A: 40.5, Company B: 43)
- Range (Company A: 25, Company B: 22)
Now we analyze the statements:
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The mean age of employees from Company A is higher than the mean age of employees from Company B.
- This is false (42.75 < 44.25).
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The median age of employees from Company A is lower than the median age of employees from Company B.
- This is true (40.5 < 43).
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The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
- This is true (25 > 22).
Based on the analysis:
- Statement 1: False
- Statement 2: True
- Statement 3: True
The correct option is statements 2 and 3.