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?
The mean age of employees from Company A is higher than the mean age of employees from Company B.
The median age of employees from Company A is lower than the median age of employees from Company B.
The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
(1 point)
Responses
statements 1 and 3
statements 1, 2, and 3
statements 2 and 3
statements 1 and 2
statement 1
statements 1 and 3
statements 1, 2, and 3
statements 2 and 3
statements 1 and 2
which of these
The answer is "statements 1 and 3".
To determine which statement is true, we need to compare the mean, median, and range of ages for employees from Company A and Company B. Let's calculate these values step-by-step.
1. Mean Age:
To find the mean age of each company, we add up all the ages and divide by the total number of employees.
For Company A:
Sum of ages = 34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38 = 634
Total employees = 16
Mean age = Sum of ages / Total employees = 634 / 16 = 39.625
For Company B:
Sum of ages = 29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48 = 620
Total employees = 16
Mean age = Sum of ages / Total employees = 620 / 16 = 38.75
2. Median Age:
To find the median age of each company, we need to arrange the ages in ascending order and find the middle value.
For Company A:
Arranged ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
Median age = Middle value = (40 + 41) / 2 = 40.5
For Company B:
Arranged ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 49, 51, 52
Median age = Middle value = (43 + 44) / 2 = 43.5
3. Range:
To find the range of ages, we subtract the minimum age from the maximum age.
For Company A:
Range = Maximum age - Minimum age = 52 - 27 = 25
For Company B:
Range = Maximum age - Minimum age = 52 - 29 = 23
Now, let's compare the statements:
Statement 1: The mean age of employees from Company A is higher than the mean age of employees from Company B.
The mean age of Company A is 39.625, which is higher than the mean age of Company B, which is 38.75. Therefore, statement 1 is true.
Statement 2: The median age of employees from Company A is lower than the median age of employees from Company B.
The median age of Company A is 40.5, which is higher than the median age of Company B, which is 43.5. Therefore, statement 2 is false.
Statement 3: The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
The range of ages for Company A is 25, which is higher than the range of ages for Company B, which is 23. Therefore, statement 3 is true.
Based on the comparisons, the correct answer is: statements 1 and 3.