Question

Weighted Mean A student of the author earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned grades of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60% of the final grade, the final exam counts for 10%, the project counts for 15%, and homework counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D, or F)? Assume that a

mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on

Short answer

The grade point average is 81.2, and the letter grade is B.

Step-by-step solution

Given information

• The marks obtained by the student in five regular tests are 63, 91, 88, 84, and 79. The score of 86 was earned on the final exam and 90 on class projects, resulting in a combined grade of 70.
• The proportion of weight from all exams is 60% from the final grade, 10% from the final exam, 15% from the project count, and 15% from the homework count.

Describe the weights and data points

Letx be the score of students in different exams or projects.

The associated weights for each exam are represented by w.

The weighted mean formula is stated as follows.

$\overline{x}=\frac{\sum \left(w\times x\right)}{\sum w}$

Identify the weights associated with values

Here, 60% weightage is given to the five regular tests, that is, the average of the test scores.

The average of five test scores is computed as follows.

$$\begin{gathered} {\overline{x}}_R=\frac{\sum x_i}{n} \\ =\frac{63+91+88+84+79}{5} \\ =\frac{405}{5} \\ =81 \end{gathered}$$

The weights associated with the scores are tabulated as follows.

x	w
81	0.6
86	0.1
90	0.15
70	0.15

Compute the weighted mean

Substitute the values in the formula.

$$\begin{gathered} \overline{x}=\frac{\sum x\times w}{\sum w} \\ =\frac{81\times 0.6+86\times 0.1+90\times 0.15+70\times 0.15}{0.6+0.1+0.15+0.15} \\ =\frac{48.6+8.6+13.5+10.5}{1} \\ =81.2 \end{gathered}$$

Thus, the weighted average is 81.2.

Assume the following grade criteria.

A	Above 90
B	80–89
C	70–79

Thus, the letter grade earned by the student is B.