Question
What is the formula to calculate the total mark of a student's science test when the categories and their respective weights are provided?
Answers
Answered by
GPT-4o mini
To calculate the total mark of a student's science test when categories and their respective weights are provided, you can use the following formula:
\[
\text{Total Mark} = \sum_{i=1}^{n} ( \text{Score}_i \times \text{Weight}_i )
\]
Where:
- \( n \) is the total number of categories (e.g., quizzes, lab work, projects, exams, etc.).
- \( \text{Score}_i \) is the score obtained in category \( i \).
- \( \text{Weight}_i \) is the weight of category \( i \) (expressed as a decimal, where 1 represents 100%).
However, you may need to normalize the weights to make sure they add up to 1. If the weights do not sum to 1, you can normalize them using the following procedure:
1. Calculate the total weight:
\[
\text{Total Weight} = \sum_{i=1}^{n} \text{Weight}_i
\]
2. Normalize the weights for each category:
\[
\text{Normalized Weight}_i = \frac{\text{Weight}_i}{\text{Total Weight}}
\]
3. Substitute the normalized weights back into the total mark formula:
\[
\text{Total Mark} = \sum_{i=1}^{n} ( \text{Score}_i \times \text{Normalized Weight}_i )
\]
Using this approach, you can compute the overall score based on the individual scores and their respective weights.
\[
\text{Total Mark} = \sum_{i=1}^{n} ( \text{Score}_i \times \text{Weight}_i )
\]
Where:
- \( n \) is the total number of categories (e.g., quizzes, lab work, projects, exams, etc.).
- \( \text{Score}_i \) is the score obtained in category \( i \).
- \( \text{Weight}_i \) is the weight of category \( i \) (expressed as a decimal, where 1 represents 100%).
However, you may need to normalize the weights to make sure they add up to 1. If the weights do not sum to 1, you can normalize them using the following procedure:
1. Calculate the total weight:
\[
\text{Total Weight} = \sum_{i=1}^{n} \text{Weight}_i
\]
2. Normalize the weights for each category:
\[
\text{Normalized Weight}_i = \frac{\text{Weight}_i}{\text{Total Weight}}
\]
3. Substitute the normalized weights back into the total mark formula:
\[
\text{Total Mark} = \sum_{i=1}^{n} ( \text{Score}_i \times \text{Normalized Weight}_i )
\]
Using this approach, you can compute the overall score based on the individual scores and their respective weights.