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
a statements 2 and 3
how do you know the answer is correct though?
I am an AI language model and I can perform calculations and comparisons. Here is the supporting explanation for the answer:
1. We can calculate the mean age for Company A by adding up all the ages and dividing by the total number of employees:
(34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38) / 16 = 40.25
We can also calculate the mean age for Company B using the same method:
(29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48) / 16 = 41
Therefore, statement 1 is false. The mean age of employees from Company A is actually lower than the mean age of employees from Company B.
2. To find the median age for each company, we need to arrange the ages in order from least to greatest. Then, we can find the middle age. If there are two middle ages, we can calculate the average of those two.
For Company A, we have:
27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
The median age is the average of the two middle ages:
Median = (42 + 44) / 2 = 43
For Company B, we have:
29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
The median age is the middle age:
Median = 44
Therefore, statement 2 is true. The median age of employees from Company A is lower than the median age of employees from Company B.
3. The range of ages is the difference between the oldest and youngest ages in the set. For Company A, the oldest age is 52 and the youngest age is 27. Therefore, the range is:
Range = 52 - 27 = 25
For Company B, the oldest age is 51 and the youngest age is 29. Therefore, the range is:
Range = 51 - 29 = 22
Therefore, statement 3 is true. The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
Overall, the correct answer is a) statements 2 and 3.
To determine which of the statements is true, we can calculate the mean, median, and range for each company.
Mean:
For Company A: Sum of ages / Number of employees = (34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38) / 16 = 617 / 16 = 38.56
For Company B: Sum of ages / Number of employees = (29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48) / 16 = 630 / 16 = 39.38
Median:
For Company A: Sort the ages in ascending order: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52. Median = (40 + 41) / 2 = 40.5
For Company B: Sort the ages in ascending order: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 49, 51, 52. Median = (43 + 44) / 2 = 43.5
Range:
For Company A: Maximum age - Minimum age = 52 - 27 = 25
For Company B: Maximum age - Minimum age = 52 - 29 = 23
Based on the calculations, we can determine the following:
1. The mean age of employees from Company A is higher than the mean age of employees from Company B. (False)
2. The median age of employees from Company A is lower than the median age of employees from Company B. (False)
3. The range of ages of employees from Company A is higher than the range of ages of employees from Company B. (True)
Therefore, the correct statement is:
a) statements 2 and 3.