The 2 different data sets below shows the ages of patients seen by two doctors in a family clinic in one day. Compare the ages of the patients of Doctor 1 and Doctor 2 using the mean and the median of each data set. SHOW ALL OF YOUR WORK!
Ages of Doctor 1's Patients:
1, 1, 2, 3, 7, 9, 15, 17, 18, 20, 22, 29
Ages of Doctor 2's Patients:
2, 2, 3, 9, 13, 17, 20, 20, 22, 23, 26, 35
First, let's find the mean and median of each data set.
Doctor 1's patients:
1, 1, 2, 3, 7, 9, 15, 17, 18, 20, 22, 29
To calculate the mean, add all the ages together and then divide by the number of patients:
(1+1+2+3+7+9+15+17+18+20+22+29) / 12
= 144 / 12
= 12
Mean age of Doctor 1's patients = 12 years old
To calculate the median, find the middle value of the ordered data set. Since there are 12 values, the median will be the average of the 6th and 7th values:
(7+9) / 2
= 16 / 2
= 8
Median age of Doctor 1's patients = 8 years old
Doctor 2's patients:
2, 2, 3, 9, 13, 17, 20, 20, 22, 23, 26, 35
To calculate the mean, add all the ages together and then divide by the number of patients:
(2+2+3+9+13+17+20+20+22+23+26+35) / 12
= 192 / 12
= 16
Mean age of Doctor 2's patients = 16 years old
To calculate the median, find the middle value of the ordered data set. Since there are 12 values, the median will be the average of the 6th and 7th values:
(17+20) / 2
= 37 / 2
= 18.5
Median age of Doctor 2's patients = 18.5 years old
In conclusion, the mean age of Doctor 1's patients is 12 years old and the median age is 8 years old, while the mean age of Doctor 2's patients is 16 years old and the median age is 18.5 years old. This means Doctor 2's patients tend to be older than Doctor 1's patients.