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In year 2001, which of the following courses had enrolments most near
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13 Jun 2025, 03:09
13 Jun 2025, 03:09
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In year 2001, which of the following courses had enrolments most nearly equal to the average (arithmetic mean) enrolments per course?
(A) Science
(B) Physical Education
(C) Commerce
(D) Applied Sciences
(E) Vocational
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Re: In year 2001, which of the following courses had enrolments most near
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15 Jun 2025, 01:57
15 Jun 2025, 01:57
1
we know mean=avg=total sum/ number of elements
here we the number of elements are courses and there are 10 courses mentioned.
so avg=total enrollments/course=50,000/10 hence 5000,
so answer is
now 5000 is 10% of total enrollments so answer is the course which is around 10% of overall enrollments
so 10% as mentioned science is the answer.
here we the number of elements are courses and there are 10 courses mentioned.
so avg=total enrollments/course=50,000/10 hence 5000,
so answer is
now 5000 is 10% of total enrollments so answer is the course which is around 10% of overall enrollments
so 10% as mentioned science is the answer.
Re: In year 2001, which of the following courses had enrolments most near
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15 Jun 2025, 04:00
15 Jun 2025, 04:00
Expert Reply
Step 1: Calculate Total Enrolments in 2001
Total enrolments = 50,000 students.
Step 2: Identify All Courses and Their Enrolments (2001)
From the data:
- Mathematics (subcategories):
- Technical: 5.40\% + 5.10\% = 10.50\%
- Commercial: 10.30\%
- Physical Education: 9.30\%
- Humanities: 2\%
- Science: 20\%
- Applied Science: 19.2\%
- Arts \& Crafts (subcategories):
- General: 5.00\%
- Mechanical: 3.70\%
- Vocational: 20\%
Total \% accounted for:
$\(10.5+10.3+9.3+2+20+19.2+5+3.7+20=100 \%\)$ (valid).
Step 3: Compute Average Enrolments Per Course
- Number of courses: 9 (as listed above).
- Average enrolments per course:
$$
\(\frac{\text { Total enrolments }}{\text { Number of courses }}=\frac{50,000}{9} \approx 5,555.56 \text { students. }\)
$$
Step 4: Calculate Enrolments for Each Course
Multiply each course's percentage by 50,000:
\(\begin{tabular}{|l|l|l|}
\hline Course & Percentage & Enrolments (students) \\
\hline Technical (Math) & 10.50\% & $50,000 \times 0.105=5,250$ \\
\hline Commercial & 10.30\% & $50,000 \times 0.103=5,150$ \\
\hline Physical Education & 9.30\% & $50,000 \times 0.093=4,650$ \\
\hline Humanities & 2\% & $50,000 \times 0.02=1,000$ \\
\hline Science & 20\% & $50,000 \times 0.20=10,000$ \\
\hline Applied Science & 19.2\% & $50,000 \times 0.192=9,600$ \\
\hline Arts \& Crafts (General) & 5\% & $50,000 \times 0.05=2,500$ \\
\hline Mechanical & 3.70\% & $50,000 \times 0.037=1,850$ \\
\hline Vocational & 20\% & $50,000 \times 0.20=10,000$ \\
\hline
\end{tabular}\)
Step 5: Compare Enrolments to the Average $(\sim 5,555.56)$
Find the course with enrolments closest to 5,555.56:
\(\begin{tabular}{|l|l|l|}
\hline Course & Enrolments & Difference from Average \\
\hline Technical (Math) & 5,250 & $5,555.56-5,250=305.56$ \\
\hline Commercial & 5,150 & $5,555.56-5,150=405.56$ \\
\hline Physical Education & 4,650 & $5,555.56-4,650=905.56$ \\
\hline Science & 10,000 & $10,000-5,555.56=4,444.44$ \\
\hline Applied Science & 9,600 & $9,600-5,555.56=4,044.44$ \\
\hline Vocational & 10,000 & $10,000-5,555.56=4,444.44$ \\
\hline
\end{tabular}\)
Smallest difference: Technical (Math) with 305.56, followed by Commercial with 405.56.
Step 6: Verify for "Commercial"
The question lists Commerce (likely referring to Commercial in the data). Its enrolments $(5,150)$ are closer to the average than Physical Education, Science, Applied Science, or Vocational.
Final Answer:
Commercial (with 5,150 enrolments) is the course most nearly equal to the average enrolments per course (~5,555.56).
Total enrolments = 50,000 students.
Step 2: Identify All Courses and Their Enrolments (2001)
From the data:
- Mathematics (subcategories):
- Technical: 5.40\% + 5.10\% = 10.50\%
- Commercial: 10.30\%
- Physical Education: 9.30\%
- Humanities: 2\%
- Science: 20\%
- Applied Science: 19.2\%
- Arts \& Crafts (subcategories):
- General: 5.00\%
- Mechanical: 3.70\%
- Vocational: 20\%
Total \% accounted for:
$\(10.5+10.3+9.3+2+20+19.2+5+3.7+20=100 \%\)$ (valid).
Step 3: Compute Average Enrolments Per Course
- Number of courses: 9 (as listed above).
- Average enrolments per course:
$$
\(\frac{\text { Total enrolments }}{\text { Number of courses }}=\frac{50,000}{9} \approx 5,555.56 \text { students. }\)
$$
Step 4: Calculate Enrolments for Each Course
Multiply each course's percentage by 50,000:
\(\begin{tabular}{|l|l|l|}
\hline Course & Percentage & Enrolments (students) \\
\hline Technical (Math) & 10.50\% & $50,000 \times 0.105=5,250$ \\
\hline Commercial & 10.30\% & $50,000 \times 0.103=5,150$ \\
\hline Physical Education & 9.30\% & $50,000 \times 0.093=4,650$ \\
\hline Humanities & 2\% & $50,000 \times 0.02=1,000$ \\
\hline Science & 20\% & $50,000 \times 0.20=10,000$ \\
\hline Applied Science & 19.2\% & $50,000 \times 0.192=9,600$ \\
\hline Arts \& Crafts (General) & 5\% & $50,000 \times 0.05=2,500$ \\
\hline Mechanical & 3.70\% & $50,000 \times 0.037=1,850$ \\
\hline Vocational & 20\% & $50,000 \times 0.20=10,000$ \\
\hline
\end{tabular}\)
Step 5: Compare Enrolments to the Average $(\sim 5,555.56)$
Find the course with enrolments closest to 5,555.56:
\(\begin{tabular}{|l|l|l|}
\hline Course & Enrolments & Difference from Average \\
\hline Technical (Math) & 5,250 & $5,555.56-5,250=305.56$ \\
\hline Commercial & 5,150 & $5,555.56-5,150=405.56$ \\
\hline Physical Education & 4,650 & $5,555.56-4,650=905.56$ \\
\hline Science & 10,000 & $10,000-5,555.56=4,444.44$ \\
\hline Applied Science & 9,600 & $9,600-5,555.56=4,044.44$ \\
\hline Vocational & 10,000 & $10,000-5,555.56=4,444.44$ \\
\hline
\end{tabular}\)
Smallest difference: Technical (Math) with 305.56, followed by Commercial with 405.56.
Step 6: Verify for "Commercial"
The question lists Commerce (likely referring to Commercial in the data). Its enrolments $(5,150)$ are closer to the average than Physical Education, Science, Applied Science, or Vocational.
Final Answer:
Commercial (with 5,150 enrolments) is the course most nearly equal to the average enrolments per course (~5,555.56).
