Question 1105416: One school has the following distribution of students by age group:
age range: (0-4) (4-6) (6-10) (10-16) (16-18) Total
absolute frequency: 20 | 50 | 100 | 120 | 110 | 400
a) Estimate the average age of the students.
b) Suppose there are two incentive policies for schools: one that favors early childhood education, another that favors secondary education. The incentive to early childhood education provides a sum of R $ 500 per enrolled child aged 5 years or less; for high school, 150 reais are offered per student aged 16 or over.
With the current age distribution, how much will the school receive in total, incentive? Justify.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! (0-4) (4-6) (6-10) (10-16) (16-18) Total
20 | 50 | 100 | 120 | 110 | 400
middle range is 2*20+5*50+8*100+13*120+17*110
This is 40+250+800+1560+1870=4520
divide by 400
average age is 11.3
With the age distribution 16 and older, the conservative way is to use the 110 in the group or 16,500 Rs.
This misses some of the age group 10-16, which could be changed by having the groups either include the top number or not include it. If included, those 16 and older wouldn't be counted. If not, those who were 16 would be counted in the oldest group. The 5 and under would be 70*500=35,000 Rs. This would take the whole group, even 6 year-olds but is fair as the average is counted.
One just has to realize that the middle of the second group sets the average and the whole group is then considered 5 and under. The oldest group is probably better left alone with none from the second highest.
The total I would calculate is 51,500 Rs.
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