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.
1. The mean age of employees from Company A is 41.2 and the mean age of employees from Company B is 40.5. Therefore, statement 1 is false.
2. The median age of employees from Company A is 40.5 and the median age of employees from Company B is 43.5. Therefore, statement 2 is true.
3. The range of ages of employees from Company A is 25 (from 27 to 52) and the range of ages of employees from Company B is 22 (from 29 to 51). Therefore, statement 3 is false.
To determine which of the statements is true, let's compare the mean, median, and range of ages for employees from Company A and Company B individually.
For Company A:
Ages: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
1. Mean: To find the mean, we sum up all the ages and divide by the total number of employees.
Mean = (34+28+36+27+45+44+30+42+41+40+50+48+52+45+39+38)/16
Mean = 599/16
Mean ≈ 37.44
2. Median: To find the median, we need to sort the ages in ascending order and find the middle value or average of two middle values if the total is even.
Sorted ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
Median = (40 + 41)/2
Median = 40.5
3. Range: The range is the difference between the highest and lowest ages in the data set.
Range = 52 - 27
Range = 25
Now let's calculate the mean, median, and range for Company B:
For Company B:
Ages: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48
1. Mean:
Mean = (29+32+48+51+49+37+33+35+36+40+45+48+43+43+44+48)/16
Mean = 625/16
Mean ≈ 39.06
2. Median:
Sorted ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
Median = 43
3. Range:
Range = 51 - 29
Range = 22
Now let's evaluate the statements:
1. The mean age of employees from Company A is higher than the mean age of employees from Company B.
Mean for Company A ≈ 37.44, Mean for Company B ≈ 39.06
Statement 1 is false.
2. The median age of employees from Company A is lower than the median age of employees from Company B.
Median for Company A = 40.5, Median for Company B = 43
Statement 2 is false.
3. The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
Range for Company A = 25, Range for Company B = 22
Statement 3 is true.
Therefore, the correct statement is:
3. The range of ages of employees from Company A is higher than the range of ages of employees from Company B.