The Table below is taken from the Australian Government’s Department of Educatio
ID: 3301929 • Letter: T
Question
The Table below is taken from the Australian Government’s Department of Education and Training. It provides data on number of offers made to high school graduates for admission into Australian university programs in various fields of education (discipline). The data is taken from the website https://docs.education.gov.au/documents/undergraduate-applications-and-offers-february-2016. Students having the best academic grade in high school would be in the ATAR band 90.05 or more, and the worst in the band 50.00 or less.
1. Based on the proportion of offers made for different grades, which discipline is the most popular for the best students and what is that proportion?
2. If an Australian student is selected at random, then from the table above, what is the probability that he or she is studying “Society and Culture” and had an ATAR score of 80.00 or less?
3. Based on the proportion of offers made, which discipline has the highest proportion of students with the lowest ATAR grades, and what is that proportion?
4. Which discipline has majority of the students from “No ATAR/Non-Yr 12” background? Please find out the reasons for that through internet searches?
Table 11: Share of Year 12 offers by ATAR band for each field of education, February 2016 90.05 or No ATAR/ 8 2 50.00 or less 70.05- 80.00 80.05 0 60.00 70.00 3 Physical Sciences Engineering and Architecture and Environmental and Related Studies Management and Society and Culture Note: Hospitality and Mixed Field Programs are not shown due to the small number of offers, hence the total number of offers does not equal the sum of offers by broad field of education in the aboveExplanation / Answer
1. Based on the proportion of offers made for different grades, which discipline is the most popular for the best students and what is that proportion?
Answer: Best students are in the ATAR band 90.05 or more. Total offers made in this column are 34,736.
Society and Culture has maximum offers in this column = 8180. So, proportion of offers to Society and Culture is = 8180 / 34736 = 0.235 = 23.5%
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2. If an Australian student is selected at random, then from the table above, what is the probability that he or she is studying “Society and Culture” and had an ATAR score of 80.00 or less?
Answer: P( studying “Society and Culture” & ATAR score of 80.00 or less) =?
Sum all offers in the row Society and Culture which have ATAR score 80 or less = 2814+2807+3806+5030 = 14457
Total offers = 22160
So, P( studying “Society and Culture” & ATAR score of 80.00 or less) = 14457 / 22160 = 0.6523
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3. Based on the proportion of offers made, which discipline has the highest proportion of students with the lowest ATAR grades, and what is that proportion?
Answer: Of the total offers made by any discipline, Education has 7.3% offers made to students with lowest grades 50.0 or less. All other disciplines have a lower proportion than this. This is the highest percentage in column of 50.0 or less.
NOTE: Actual count of offers made by any discipline in first column is highest for society and culture which is 2814, but here we want the comparison based on proportion of offers, and not the count of offers.
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4. Which discipline has majority of the students from “No ATAR/Non-Yr 12” background? Please find out the reasons for that through internet searches?
Answer: "Health" has 57.2% students from No ATR background.
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