Economic ConditionsIntelligence level
Bright
Average
Dull
Borderline
Good
55
81
59
140
Poor
50
73
84
101  
What proportion of total students are dull?

To determine the proportion of students categorized as "dull," we need to find the total number of students and then calculate the ratio of "dull" students to this total.

Here are the given numbers of students based on intelligence levels and economic conditions:

- Bright: 55 (Good) + 50 (Poor) = 105
- Average: 81 (Good) + 73 (Poor) = 154
- Dull: 59 (Good) + 84 (Poor) = 143
- Borderline: 140 (Good) + 101 (Poor) = 241

Let's sum these numbers to get the total number of students:

\[ \text{Total number of students} = 105 + 154 + 143 + 241 \]

\[ \text{Total number of students} = 643 \]

Now, the number of "dull" students is 143. To find the proportion of "dull" students, we divide the number of "dull" students by the total number of students:

\[ \text{Proportion of dull students} = \frac{143}{643} \]

\[ \text{Proportion of dull students} \approx 0.2224 \]

Therefore, the proportion of total students who are "dull" is approximately 0.2224 or 22.24%.

Would you like more details or have any questions about this calculation? Here are some additional questions you might find interesting:

1. What is the proportion of bright students among the total?
2. How many students fall into the "borderline" intelligence category?
3. What is the total number of students with good economic conditions?
4. What is the total number of students with poor economic conditions?
5. What is the ratio of bright students to dull students?
6. How does the proportion of average students compare to the proportion of borderline students?
7. What percentage of students are categorized as bright or average?
8. How many more students are in the borderline category compared to the bright category?

**Tip:** When calculating proportions, always ensure that you have the correct total before performing the division to avoid errors in your final result.

Learn how to calculate the proportion of "dull" students among different economic conditions based on given data. This problem involves statistics and proportions, determining ratios based on intelligence levels and economic status. Suitable for students in Grades 9-12.

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