The ages of randomly selected employees at two companies are recorded. Their ages are as follows.
Company A: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
Company B: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
Which of the following statements is true?
1. The mean age of employees from Company A is higher than the mean age of employees from Company B.
2. The median age of employees from Company A is lower than the median age of employees from Company B.
3. The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
A. statements 2 and 3
B. statements 1 and 3
C. statements 1 and 2
D. statements 1, 2, and 3
B. statements 1 and 3 (The mean age of employees from Company A is higher than the mean age of employees from Company B, and the range of ages of employees from Company A is higher than the range of ages of employees from Company B. Statement 2 is false; the median age of employees from Company A is 40, while the median age of employees from Company B is 43.)
To determine which of the statements is true, we can calculate the mean, median, and range for each company's employee ages.
For Company A:
Mean age = (34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38)/16 ≈ 40.5
Median age = (38 + 39)/2 = 38.5
Range = 52 - 27 = 25
For Company B:
Mean age = (29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48)/16 ≈ 41.8125
Median age = (40 + 43)/2 = 41.5
Range = 51 - 29 = 22
Comparing the calculated values:
1. The mean age of employees from Company A is 40.5, while the mean age of employees from Company B is 41.8125. Therefore, statement 1 is false.
2. The median age of employees from Company A is 38.5, while the median age of employees from Company B is 41.5. Therefore, statement 2 is false.
3. The range of ages of employees from Company A is 25, while the range of ages of employees from Company B is 22. Therefore, statement 3 is true.
Based on the calculations, the only true statement is statement 3. Therefore, the answer is A. statements 2 and 3.