College A B C D E Demand (application received) 3000 600 2500 1200 3300 Intake (available seats) 1500 1800 1000 2700 2200
This question requires us to compare the average demand for seats in five colleges against the average available seats (intake) across these same colleges. We need to find out by what percentage the average demand exceeds the average intake.
Data Analysis: Demand and Intake in Five Colleges
First, let's organize the data provided in the table:
| College | Demand (application received) | Intake (available seats) |
| A | 3000 | 1500 |
| B | 600 | 1800 |
| C | 2500 | 1000 |
| D | 1200 | 2700 |
| E | 3300 | 2200 |
Calculating Average Demand
To find the average demand, we sum the demand from all five colleges and divide by the number of colleges (which is 5).
Total Demand = Demand(A) + Demand(B) + Demand(C) + Demand(D) + Demand(E)
Total Demand = 3000 + 600 + 2500 + 1200 + 3300 = 10600 applications
Average Demand = \(\frac{Total \, Demand}{Number \, of \, Colleges}\)
Average Demand = \(\frac{10600}{5}\) = 2120 applications
Calculating Average Intake
Similarly, to find the average intake, we sum the available seats from all five colleges and divide by 5.
Total Intake = Intake(A) + Intake(B) + Intake(C) + Intake(D) + Intake(E)
Total Intake = 1500 + 1800 + 1000 + 2700 + 2200 = 9200 seats
Average Intake = \(\frac{Total \, Intake}{Number \, of \, Colleges}\)
Average Intake = \(\frac{9200}{5}\) = 1840 seats
Determining Percentage Difference
Now we need to find how much percent more the average demand is than the average intake. First, calculate the difference between the average demand and the average intake.
Difference = Average Demand - Average Intake
Difference = 2120 - 1840 = 280
To express this difference as a percentage of the average intake, we use the following formula:
Percentage Increase = \(\frac{Difference}{Average \, Intake} \times 100\%\)
Percentage Increase = \(\frac{280}{1840} \times 100\%\)
Percentage Increase = \(\frac{28}{184} \times 100\%\)
Percentage Increase = \(\frac{7}{46} \times 100\%\)
Percentage Increase ≈ 0.1521739... \(\times 100\%\)
Percentage Increase ≈ 15.21739... %
Rounding this to two decimal places, we get 15.22%.
Conclusion
The average demand of all five colleges is approximately 15.22% more than the average of the available seats.
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