To analyze the statements about the ages of employees from Company A and Company B, we need to calculate the mean, median, and range of the ages for both companies.
Company A Ages:
Ages: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
Calculating Mean: \[ \text{Mean} = \frac{\sum \text{ages}}{\text{number of ages}} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = \frac{680}{16} = 42.5 \]
Calculating 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 ages (even), the median is the average of the 8th and 9th numbers: \[ \text{Median} = \frac{40 + 41}{2} = 40.5 \]
Calculating 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
Calculating Mean: \[ \text{Mean} = \frac{\sum \text{ages}}{\text{number of ages}} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} = \frac{736}{16} = 46 \]
Calculating 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 ages (even), the median is the average of the 8th and 9th numbers: \[ \text{Median} = \frac{43 + 43}{2} = 43 \]
Calculating Range: \[ \text{Range} = \text{max} - \text{min} = 51 - 29 = 22 \]
Summary of Findings:
- Mean Age:
- Company A: 42.5
- Company B: 46
- Median Age:
- Company A: 40.5
- Company B: 43
- Range:
- Company A: 25
- Company B: 22
Evaluation of Statements:
-
The mean age of employees from Company A is higher than the mean age of employees from Company B.
False (42.5 < 46) -
The median age of employees from Company A is lower than the median age of employees from Company B.
True (40.5 < 43) -
The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
True (25 > 22)
Conclusion:
The true statements are 2 and 3. Therefore, the correct response is:
statements 2 and 3