Assignments (weight 40%)
Exams (weight 60%)
A student scores:
75 in assignments
85 in exams
What is the student's weighted arithmetic mean score?
Calculating Student Weighted Mean Score
The weighted arithmetic mean is used to calculate the final performance score when different components have different importance (weights).
Weighted Mean Formula
The formula for the weighted arithmetic mean is:
$ \text{Weighted Mean} = \sum_{i=1}^{n} (x_i \cdot w_i) $
Where:
- \( x_i \) is the score for the \( i^{th} \) component.
- \( w_i \) is the weight (as a decimal) for the \( i^{th} \) component.
- \( n \) is the number of components.
Applying the Formula
In this case:
- Component 1: Assignments
- Score (\( x_1 \)): 75
- Weight (\( w_1 \)): 40% or 0.40
- Component 2: Exams
- Score (\( x_2 \)): 85
- Weight (\( w_2 \)): 60% or 0.60
Step-by-Step Calculation
- Convert the weights from percentages to decimals:
- Assignments: \( 40\% = 0.40 \)
- Exams: \( 60\% = 0.60 \)
- Multiply each score by its corresponding weight:
- Assignments contribution: \( 75 \times 0.40 = 30 \)
- Exams contribution: \( 85 \times 0.60 = 51 \)
- Sum the contributions from each component to find the weighted mean score:
- Total Score = \( 30 + 51 = 81 \)
Final Result
The student's weighted arithmetic mean score is 81.
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
