A class has 100 students. In a group with 80 students the average number of days they are absent is 4 and in the other group of 20 the average number of days students are absent is 6. What is the average number of days students are absent in the entire class. Please explain.
The class has 100 students in all. It can be divided into 2 groups with 80 and 20 students respectively. The average number of days students are absent in the first group is 4 and in the second it is 6.
To determine the average number of days students in the entire class are absent it is not possible to take the average of 4 and 6. The reason behind this is that the number of students in each of the groups is different. The correct way of arriving at the average for the class is to take the weighted average of the two groups.
This is equal to `(80*4 + 20*6)/(80+20)= (320+120)/100 = 4.4`
When determining the weighted average what is basically being done is calculating the total number of days that students in the class are absent and divide that by the total number of students.