The following table shows the number of students admitted (A) and left (L)…
2022
The following table shows the number of students admitted (A) and left (L) from the five different colleges (P-T) during the years 2016-2021. Year of foundation of all the five colleges is 2016. Based on the data in the table, answer the questions 1-5:
Year-wise Distribution of Students
Year | P A | P L | Q A | Q L | R A | R L | S A | S L | T A | T L |
|---|---|---|---|---|---|---|---|---|---|---|
2016 | 2250 | - | 2100 | - | 2400 | - | 3200 | - | 3100 | - |
2017 | 660 | 440 | 900 | 500 | 840 | 460 | 880 | 500 | 700 | 450 |
2018 | 580 | 420 | 650 | 430 | 800 | 500 | 800 | 520 | 760 | 460 |
2019 | 690 | 400 | 570 | 420 | 720 | 450 | 790 | 440 | 820 | 440 |
2020 | 760 | 500 | 600 | 380 | 680 | 480 | 840 | 450 | 880 | 420 |
2021 | 700 | 460 | 680 | 440 | 820 | 560 | 920 | 480 | 850 | 430 |
The average number of students studying in all the five colleges (P-T) in the year 2018 is
Answer: B. 3188 — CONCEPTFor a group whose membership changes over time, the number present at the end of a period equals the opening number plus admissions minus departures.…
- A.
3168
- B.
3188
- C.
3148
- D.
3388
Attempted by 1 students.
Show answer & explanation
Correct answer: B
CONCEPT
For a group whose membership changes over time, the number present at the end of a period equals the opening number plus admissions minus departures. Apply this update cumulatively for every year up to the target year.
The arithmetic mean of n group values is their total divided by n.
APPLICATION
Because every college was founded in 2016, its 2016 admissions form its opening population. Update each college through 2017 and 2018:
P: 2250 + (660 - 440) + (580 - 420) = 2630.
Q: 2100 + (900 - 500) + (650 - 430) = 2720.
R: 2400 + (840 - 460) + (800 - 500) = 3080.
S: 3200 + (880 - 500) + (800 - 520) = 3860.
T: 3100 + (700 - 450) + (760 - 460) = 3650.
Total in 2018 = 2630 + 2720 + 3080 + 3860 + 3650 = 15940.
Average = 15940 / 5 = 3188.
CROSS-CHECK
The 2016 total is 2250 + 2100 + 2400 + 3200 + 3100 = 13050.
The 2017 net increase is (660 + 900 + 840 + 880 + 700) - (440 + 500 + 460 + 500 + 450) = 3980 - 2350 = 1630.
The 2018 net increase is (580 + 650 + 800 + 800 + 760) - (420 + 430 + 500 + 520 + 460) = 3590 - 2330 = 1260.
Therefore, the 2018 total is 13050 + 1630 + 1260 = 15940, and the average is 15940 / 5 = 3188.
Therefore, the average number of students studying in the five colleges in 2018 is 3188.