Marks secured by 42 students in Economics are: [Marks: 15, 20, 22, 23, 27, 35, 18; Number of Students: 8, 4, 7, 3, 8, 7, 5]. Find average marks.
Understand the Problem
The question asks to find the average marks secured by 42 students in Economics, given the marks and the number of students who secured those marks. We need to calculate the weighted average of the marks.
Answer
$23.2$
Answer for screen readers
The average mark is $23.2$.
Steps to Solve
- Calculate the product of marks and the number of students for each mark
Multiply the marks by the corresponding number of students: $15 \times 8 = 120$ $20 \times 4 = 80$ $22 \times 7 = 154$ $23 \times 3 = 69$ $27 \times 8 = 216$ $35 \times 7 = 245$ $18 \times 5 = 90$
- Calculate the sum of these products
Add up all the products calculated in the previous step: $120 + 80 + 154 + 69 + 216 + 245 + 90 = 974$
- Calculate the average marks
Divide the sum of the products by the total number of students (42): $\text{Average Marks} = \frac{974}{42}$
- Rounding the average marks
$\text{Average Marks} = 23.190476... \approx 23.2$
The average mark is $23.2$.
More Information
The average mark of $23.2$ is the weighted average of the marks secured by the students, where the weights are the number of students securing those marks.
Tips
A common mistake is to simply average the marks (15, 20, 22, 23, 27, 35, 18) without considering the number of students who secured each mark. This would lead to an incorrect result. Another mistake is miscalculating the products or the sum of the products.
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