To determine the truth of the statements, we first 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
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Mean: \[ \text{Mean} = \frac{\sum \text{ages}}{n} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = \frac{670}{16} = 41.875 \]
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Median:
- Ordered Ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
- For 16 values, the median is the average of the 8th and 9th values: \[ \text{Median} = \frac{40 + 41}{2} = 40.5 \]
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Range: \[ \text{Range} = \text{Max} - \text{Min} = 52 - 27 = 25 \]
Company B
Ages: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
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Mean: \[ \text{Mean} = \frac{\sum \text{ages}}{n} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} = \frac{682}{16} = 42.625 \]
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Median:
- Ordered Ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
- For 16 values, the median is: \[ \text{Median} = \frac{43 + 40}{2} = 41 \]
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Range: \[ \text{Range} = \text{Max} - \text{Min} = 51 - 29 = 22 \]
Let's 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.
- Company A Mean: 41.875, Company B Mean: 42.625
- False (41.875 < 42.625)
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The median age of employees from Company A is lower than the median age of employees from Company B.
- Company A Median: 40.5, Company B Median: 41
- True (40.5 < 41)
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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.
- Company A Range: 25, Company B Range: 22
- True (25 > 22)
Based on this analysis:
- Statement 1 is false.
- Statement 2 is true.
- Statement 3 is true.
Thus, the correct choice is:
- statements 2 and 3.