To determine which of the statements is true, let's 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
-
Mean: \[ \text{Mean} = \frac{\text{Sum of ages}}{\text{Number of employees}} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = \frac{ 34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16} = \frac{ 650}{16} = 40.625 \]
-
Median:
- Sorted ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
- Since there are 16 employees, the median will be the average of the 8th and 9th ages. \[ \text{Median} = \frac{40 + 41}{2} = 40.5 \]
-
Range: \[ \text{Range} = \text{Maximum} - \text{Minimum} = 52 - 27 = 25 \]
Company B:
Ages: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
-
Mean: \[ \text{Mean} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16} = \frac{ 697}{16} = 43.5625 \]
-
Median:
- Sorted ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
- Since there are 16 employees, the median will be the average of the 8th and 9th ages. \[ \text{Median} = \frac{43 + 43}{2} = 43 \]
-
Range: \[ \text{Range} = \text{Maximum} - \text{Minimum} = 51 - 29 = 22 \]
Summary of Findings:
- Mean age of Company A: 40.625
- Mean age of Company B: 43.5625
- Median age of Company A: 40.5
- Median age of Company B: 43
- Range of Company A: 25
- Range of Company B: 22
Evaluating the Statements:
-
The mean age of employees from Company A is higher than the mean age of employees from Company B.
False: 40.625 < 43.5625 -
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 statements 2 and 3.
The correct response is: statements 2 and 3.