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.
None of the above statements is true.
- To calculate the mean age of Company A: sum all the ages and divide by the number of employees: (34+28+36+27+45+44+30+42+41+40+50+48+52+45+39+38) / 16 = 40.25
- To calculate the mean age of Company B: sum all the ages and divide by the number of employees: (29+32+48+51+49+37+33+35+36+40+45+48+43+43+44+48) / 16 = 41.5
Therefore, the mean age of employees from Company B is higher than the mean age of employees from Company A.
- To find the median age of Company A, we need to arrange the ages from lowest to highest: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52. The median is the middle value, which is 42.5 (average of 42 and 44).
- To find the median age of Company B, we also need to arrange the ages from lowest to highest: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51. The median is also 42.5 (average of 43 and 44).
Therefore, the median age of employees from Company A is the same as the median age of employees from Company B.
- The range of ages of employees in Company A is the difference between the highest and lowest ages: 52 - 27 = 25.
- The range of ages of employees in Company B is the difference between the highest and lowest ages: 51 - 29 = 22.
Therefore, the range of ages of employees in Company A is higher than the range of ages of employees in Company B.
So, none of the given statements is true.
To find the answers, let's calculate the mean, median, and range for both Company A and Company B:
For Company A:
Mean: To find the mean, we sum up all the ages and divide by the number of employees.
Sum of ages in Company A = 34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38 = 614
Number of employees in Company A = 16
Mean age of employees in Company A = 614 / 16 = 38.375
Median: To find the median, we arrange the ages in ascending order and find the middle value.
Arranging the ages in Company A in ascending order: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
Median age of employees in Company A = (38 + 39) / 2 = 38.5
Range: To find the range, we subtract the smallest age from the largest age.
Smallest age in Company A = 27
Largest age in Company A = 52
Range of ages in Company A = 52 - 27 = 25
For Company B:
Mean: To find the mean, we sum up all the ages and divide by the number of employees.
Sum of ages in Company B = 29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48 = 628
Number of employees in Company B = 16
Mean age of employees in Company B = 628 / 16 = 39.25
Median: To find the median, we arrange the ages in ascending order and find the middle value.
Arranging the ages in Company B in ascending order: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 49, 51, 52
Median age of employees in Company B = (43 + 44) / 2 = 43.5
Range: To find the range, we subtract the smallest age from the largest age.
Smallest age in Company B = 29
Largest age in Company B = 52
Range of ages in Company B = 52 - 29 = 23
Based on the calculations:
Statement 1: The mean age of employees from Company A is higher than the mean age of employees from Company B.
Mean age of employees in Company A: 38.375
Mean age of employees in Company B: 39.25
The statement is false.
Statement 2: The median age of employees from Company A is lower than the median age of employees from Company B.
Median age of employees in Company A: 38.5
Median age of employees in Company B: 43.5
The statement is true.
Statement 3: The range of ages of employees from Company A is higher than the range of ages of employees from Company B.
Range of ages in Company A: 25
Range of ages in Company B: 23
The statement is true.
Therefore, the correct answers are:
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.