Question

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 21% of your total grade, each major test is worth 22.5%, and the final exam is worth 34%. Compute the weighted average for the following scores: 81 on the lab, 75 on the first major test, 97 on the second major test, and 84 on the final exam.

Answer 1

The weighted average for the given scores is 84.27

Explanation:

The weighted average can be calculated from the formula

Weighted average =
`(\Sigma wx)/(\Sigma w)`

Where w is the weight

and x is the score

The scores are 81, 75, 97, and 84 while their respective weights are 21% (0.21), 22.5%(0.225), 22.5%(0.225), and 34%(0.34).

From the formula

Weighted average =
`(\Sigma wx)/(\Sigma w)`

Since we have four sets of values, we can write that

Weighted average =
`(\Sigma wx)/(\Sigma w)` =
`(w_(1)x_(1) + w_(2)x_(2) + w_(3)x_(3) + w_(4)x_(4))/(w_(1) + w_(2) + w_(3) + w_(4))`

Let 81, 75, 97, and 84 be
`w_(1), w_(2), w_(3),` and
`w_(4)` respectively; then

0.21, 0.225, 0.225, and 0.34 will be
`x_(1), x_(2), x_(3),` and
`x_(4)` respectively.

∴ Weighted average =
`((81)(0.21)+(75)(0.225)+ (97)(0.225) +(84)(0.34))/(0.21+0.225+0.225+0.34)`

Weighted average =
`(17.01+16.875+21.825+28.56)/(1)`

Weighted average = 84.27

Hence, the weighted average is 84.27