What is the average number of boys in the year 2023 in all the five colleges…
2024
What is the average number of boys in the year 2023 in all the five colleges taken together?
Answer: B. 2272 — Concept: The arithmetic mean of n values is their sum divided by n. In a two-way table where every college is split into a Boys column and a Girls column, an…
- A.
2270
- B.
2272
- C.
1854
- D.
2060
Show answer & explanation
Correct answer: B
Concept: The arithmetic mean of n values is their sum divided by n. In a two-way table where every college is split into a Boys column and a Girls column, an average “across the five colleges” for a single year means taking exactly one entry per college — the entry in the sub-column the stem names — adding those five entries, and dividing by 5. The other sub-column contributes nothing to that mean, and the divisor is the number of colleges, not the number of data cells standing in the row.
Application: The stem fixes the year to 2023 and the attribute to Boys, so read the 2023 row and pick out the Boys entry of each of the five colleges:
College | A | B | C | D | E |
|---|---|---|---|---|---|
Boys admitted in 2023 | 2460 | 1960 | 2340 | 2440 | 2160 |
Add colleges A and B: 2460 + 1960 = 4420.
Add college C: 4420 + 2340 = 6760.
Add college D: 6760 + 2440 = 9200.
Add college E: 9200 + 2160 = 11360.
Divide the five-college total by the number of colleges: 11360 ÷ 5 = 2272.
Cross-check: Recompute the mean by the assumed-mean method. Taking 2200 as the assumed mean, the five deviations are +260, −240, +140, +240 and −40; they sum to +360, and 360 ÷ 5 = 72, so the mean is 2200 + 72 = 2272. A second, structural check: every entry in this table is a multiple of 20, so any total of five entries is a multiple of 20 and the resulting mean must be a multiple of 4. 2272 = 4 × 568 passes that test, whereas a mean of 2270 would demand a total of 11350, which no set of five multiples of 20 can produce.
Common mis-readings to avoid:
Adding the whole 2023 row instead of the Boys sub-column gives 11360 + 9020 = 20380, whose mean of 4076 answers a different question — the average number of students, boys and girls together.
Dividing the Boys total by 10 gives 11360 ÷ 10 = 1136, which uses the number of data cells standing in the row rather than the number of colleges.
Reading down one college’s Boys column across 2018 to 2023 gives that single college’s six-year average, not a five-college average for one year.
Result: The average number of boys admitted across colleges A to E in 2023 is 2272.