Question

3.1: measures of center. find the weighted average.
in your history class, your final grade is based on four categories. the categories are tests, labs, assignments, and a final exam. suppose you earned the following grades in each of the categories; 56% on tests, 78% on labs, 46% on assignments, and 66% on the final exam. if tests are worth 22%, labs are worth 5%, assignments are worth 16%, and the final exam is worth 57%, determine your final grade in the course. record the grade below as a percentage accurate to two decimal places.
final grade:
enter an integer or decimal number more...
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Explanation:

Step1: Recall weighted - average formula

The formula for the weighted average $\bar{x}=\sum_{i = 1}^{n}w_ix_i$, where $w_i$ is the weight and $x_i$ is the value.

Step2: Identify values and weights

Let $x_1 = 56$, $w_1=0.22$ (22% as a decimal); $x_2 = 78$, $w_2 = 0.05$ (5% as a decimal); $x_3=46$, $w_3 = 0.16$ (16% as a decimal); $x_4 = 66$, $w_4=0.57$ (57% as a decimal).

Step3: Calculate the weighted - average

$\bar{x}=w_1x_1 + w_2x_2+w_3x_3 + w_4x_4$
$=0.22\times56+0.05\times78 + 0.16\times46+0.57\times66$
$=0.22\times56 = 12.32$
$0.05\times78=3.9$
$0.16\times46 = 7.36$
$0.57\times66 = 37.62$
$\bar{x}=12.32 + 3.9+7.36+37.62$
$=61.2$

Answer:

$61.20$