Do you know how to calculate a weighted average?
I was never taught how to do a weighted average. It is a very basic mathematical concept, which many teachers use to calculate a student’s grade.
A student gets a 95 on the final exam for a course and an 85 on the midterm. If the final counts for 60% of the grade and the midterm accounts for the remaining 40%, what is the overall score for the student? The numbers were chosen to simplify the calculation. Do you see a really simple way of doing the calculation in your head?
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Your scenario is easy to do in one’s head, because it is a simple average weighting of only two scores. The difference between the two scores is 10 points; weighting that difference would mean the lower score plus 60% of the difference, or 6 points added to the 85 score.
But a true weighting over time of multiple scores would be more difficult to do in one’s head.
Suppose, over a course, you weighted scores as follows:
Three quizzes count for 15% each. A mid term counts for 20%. The final counts for 35%.
It is still easy to calculate the average, but takes a bit more than doing it in one’s head.
(95*.6) + (85*.4) = 57+ 34 = 91
You can do some weighted averages in your head but spreadsheets do a good job.
I am glad to see that at least two people here are familiar with weighted averages.
Here is a problem of a type you were likely given. Do you see how it relates to weighted average? If a car travels for 3 hours at 60 mph and 2 hours at 50 mph, what was its average speed for the whole trip?
Granted it is not a very exciting problem, but seeing how it relates to weighted average should make it at least a little more interesting.
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