Question

the scores and their percent of the final grade for a statistics student are given. what is the students weighted mean score? (simplify your answer. round to two decimal places as needed.)
homework quiz quiz project final exam
score 84 81 91 95 90
percent of final grade 15 15 15 25 30

Explanation:

Step1: Recall weighted - mean formula

The formula for the weighted mean $\bar{x}=\sum_{i = 1}^{n}x_{i}w_{i}$, where $x_{i}$ is the score and $w_{i}$ is the weight (as a decimal). First, convert the percentages to decimals.

Step2: Convert percentages to decimals

Homework: $w_1 = 0.15$, Quiz 1: $w_2=0.15$, Quiz 2: $w_3 = 0.15$, Project: $w_4=0.25$, Final Exam: $w_5 = 0.30$. Scores are $x_1 = 84$, $x_2=81$, $x_3 = 91$, $x_4=95$, $x_5 = 90$.

Step3: Calculate the product of each score and its weight

$x_1w_1=84\times0.15 = 12.6$, $x_2w_2=81\times0.15=12.15$, $x_3w_3=91\times0.15 = 13.65$, $x_4w_4=95\times0.25=23.75$, $x_5w_5=90\times0.30 = 27$.

Step4: Sum up the products

$\bar{x}=12.6 + 12.15+13.65 + 23.75+27$
$\bar{x}=89.15$

Answer:

$89.15$