To determine which statements are true, we 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
Mean Age: \[ \text{Mean} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} \] \[ = \frac{704}{16} = 44 \]
Median Age: First, we arrange the ages in increasing 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: Median = (40 + 41) / 2 = 40.5
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
Mean Age: \[ \text{Mean} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} \] \[ = \frac{704}{16} = 44 \]
Median Age: Arranging ages in increasing order: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
Median = (43 + 40) / 2 = 42.5
Range: \[ \text{Range} = \text{Max} - \text{Min} = 51 - 29 = 22 \]
Summary:
- Mean Age Company A: 44
- Mean Age Company B: 44
- Median Age Company A: 40.5
- Median Age Company B: 42.5
- Range Company A: 25
- Range Company B: 22
Statements:
-
The mean age of employees from Company A is higher than the mean age of employees from Company B.
- False: Both means are the same (44).
-
The median age of employees from Company A is lower than the median age of employees from Company B.
- True: (40.5 < 42.5)
-
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. Thus, the correct answer is:
C. statements 2 and 3