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:

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.