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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.

Respuesta :

Answer:

The weighted average for the given scores is 84.27

Step-by-step explanation:

The weighted average can be calculated from the formula

Weighted average = [tex]\frac{\Sigma wx}{\Sigma w}[/tex]

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 = [tex]\frac{\Sigma wx}{\Sigma w}[/tex]

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

Weighted average = [tex]\frac{\Sigma wx}{\Sigma w}[/tex] = [tex]\frac{w_{1}x_{1} + w_{2}x_{2} + w_{3}x_{3} + w_{4}x_{4}}{w_{1} + w_{2} + w_{3} + w_{4}}[/tex]

Let 81, 75, 97, and 84 be [tex]w_{1}, w_{2}, w_{3},[/tex] and [tex]w_{4}[/tex] respectively; then

0.21, 0.225, 0.225, and 0.34 will be [tex]x_{1}, x_{2}, x_{3},[/tex] and [tex]x_{4}[/tex] respectively.

∴ Weighted average = [tex]\frac{(81)(0.21)+(75)(0.225)+ (97)(0.225) +(84)(0.34)}{0.21+0.225+0.225+0.34}[/tex]

Weighted average = [tex]\frac{17.01+16.875+21.825+28.56}{1}[/tex]

Weighted average = 84.27

Hence, the weighted average is 84.27