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
Demand for seats in a university is at its highest in the fall; demand also trends to grow and fall off in 25 year waves. In time service forecasting, the former demand characteristic would be called ______ and the latter would be called _______.
The system of combining two or more overlapping series of index numbers to obtain a single continuous series is called
The rise in the number of patients due to heatstroke is an example of:
According to government data, 24 percent of teenagers in India under the age of 18 years live in households with incomes that are classified at a particular income level. A simple random sample of 400 teenagers in India under the age of 18 years was selected for a study of learning. If the government data is correct, which of the following best approximates the probability that at least 27 per cent of the teenagers in the sample live in households that are classified at a particular income level?
Which index satisfies the factor reversal test?
