Calculating Average Students in Colleges P-T for the Year 2018

The question asks us to find the average number of students studying in all five colleges (P, Q, R, S, and T) in the year 2018. The number of students studying in a college at the end of a specific year depends on the initial number of students (foundation year) and the number of students admitted and left in subsequent years.

Since the foundation year for all colleges is 2016, the number of students at the beginning of 2016 is 0. The number of students at the end of 2016 is equal to the number of students admitted in 2016, as none left in the first year.

For any subsequent year, the number of students at the end of the year can be calculated using the formula:

$$ \text{Students (End of Year } n) = \text{Students (End of Year } n-1) + \text{Admitted in Year } n - \text{Left in Year } n $$

We need to find the number of students at the end of 2018 for each college. This requires calculating the number of students at the end of 2016 and 2017 first.

Step-by-Step Calculation of Students in Each College at the End of 2018

College P

• Students (End 2016) = Admitted (2016) = 2250
• Students (End 2017) = Students (End 2016) + Admitted (2017) - Left (2017)
• Students (End 2017) = 2250 + 660 - 440 = 2470
• Students (End 2018) = Students (End 2017) + Admitted (2018) - Left (2018)
• Students (End 2018) = 2470 + 580 - 420 = 2630

College Q

• Students (End 2016) = Admitted (2016) = 2100
• Students (End 2017) = Students (End 2016) + Admitted (2017) - Left (2017)
• Students (End 2017) = 2100 + 900 - 500 = 2500
• Students (End 2018) = Students (End 2017) + Admitted (2018) - Left (2018)
• Students (End 2018) = 2500 + 650 - 430 = 2720

College R

• Students (End 2016) = Admitted (2016) = 2400
• Students (End 2017) = Students (End 2016) + Admitted (2017) - Left (2017)
• Students (End 2017) = 2400 + 840 - 460 = 2780
• Students (End 2018) = Students (End 2017) + Admitted (2018) - Left (2018)
• Students (End 2018) = 2780 + 800 - 500 = 3080

College S

• Students (End 2016) = Admitted (2016) = 3200
• Students (End 2017) = Students (End 2016) + Admitted (2017) - Left (2017)
• Students (End 2017) = 3200 + 880 - 500 = 3580
• Students (End 2018) = Students (End 2017) + Admitted (2018) - Left (2018)
• Students (End 2018) = 3580 + 800 - 520 = 3860

College T

• Students (End 2016) = Admitted (2016) = 3100
• Students (End 2017) = Students (End 2016) + Admitted (2017) - Left (2017)
• Students (End 2017) = 3100 + 700 - 450 = 3350
• Students (End 2018) = Students (End 2017) + Admitted (2018) - Left (2018)
• Students (End 2018) = 3350 + 760 - 460 = 3650

Now, we have the number of students in each college at the end of the year 2018:

The total number of students in all five colleges at the end of 2018 is the sum of students in each college:

$$ \text{Total Students (2018)} = 2630 + 2720 + 3080 + 3860 + 3650 = 15940 $$

To find the average number of students, we divide the total number of students by the number of colleges (which is 5):

$$ \text{Average Students (2018)} = \frac{\text{Total Students (2018)}}{\text{Number of Colleges}} = \frac{15940}{5} $$

$$ \text{Average Students (2018)} = 3188 $$

Therefore, the average number of students studying in all five colleges in the year 2018 is 3188.

Revision Table: Student Data Summary

Additional Information on Data Interpretation Questions

Data interpretation questions, especially those involving tables or charts tracking changes over time like student admissions and departures, often require careful cumulative calculations. Key concepts include:

• Cumulative Totals: Understanding how values change over time, building upon previous periods. In this case, the student count at the end of a year is a cumulative figure based on admissions and departures since the college's inception.
• Net Change: The difference between admitted and left students in a year represents the net change in the student population for that year.
• Average Calculation: The average is the sum of values divided by the number of items. Here, it's the total number of students across colleges divided by the number of colleges.
• Reading Tables: Accurately extracting specific data points (like A or L values for a particular college in a specific year) from the provided table is crucial.

Such problems test your ability to track changes, perform basic arithmetic operations (addition, subtraction, division), and interpret data presented in tabular format. Always pay close attention to the specific year and colleges mentioned in the question.