A course has two quizzes of equal weight, a midterm examination that has twice the weight of a quiz, and a final examination that has twice the weight of the midterm exam. If a student obtains 54% and 60% on the quizzes; 55% on the midterm; and 80% on the final, what will be the student's weighted mean final grade?

#### Solution

Suppose the quizzes are each worth $x$. Then the midterm would be worth $2x$ and the final would be worth $4x$. As the total percent is 100 we have

$x + x +2x + 4x = 8x = 100$

That is,

$\Rightarrow x = 12.5$

Hence the weight of quizzes are each worth 12.5% of the total grade.

The midterm is worth 25% of the total grade and the final exam is worth 50% of the total grade.

The total grade

` $$ \begin{aligned} \text{weighted Grade} &=\frac{(0.125 * 0.54) + (0.125 * 0.60) + (0.25 * 0.55 ) + (0.50 * 0.80)}{100} \\ &=\frac{0.0675 + 0.0750 + 0.1375 + 0.4000}{100}\\ &= 68 \end{aligned} $$ `

Thus the weighted final grade is 68%.

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators