Weighted averages

Front

What is a weighted average?

Back

A weighted average is an average that takes into account the relative importance or weight of each value in a data set. It is calculated by multiplying each value by its weight, summing these products, and then dividing by the total weight.

Front

How do you calculate the weighted average of grades?

Back

To calculate the weighted average of grades, multiply each grade by its corresponding weight (percentage), sum these products, and then divide by the total weight.

Front

If a student has grades of 80 (40%), 90 (40%), and 100 (20%), what is their weighted average?

Back

Weighted average = (80*0.4 + 90*0.4 + 100*0.2) / (0.4 + 0.4 + 0.2) = 88.

Front

What is the formula for calculating the final grade based on weighted averages?

Back

Final Grade = (Grade1 * Weight1 + Grade2 * Weight2 + ... + GradeN * WeightN) / (Weight1 + Weight2 + ... + WeightN).

Front

In the context of averages, what does 'average' mean?

Back

Average refers to a central value of a set of numbers, typically calculated as the sum of the values divided by the number of values.

Front

What is the significance of weights in a weighted average?

Back

Weights determine the influence of each value on the final average; higher weights mean that value has more impact on the average.

Front

How do you find the average of multiple groups with different sizes?

Back

To find the average of multiple groups with different sizes, calculate the total sum of all values from each group, then divide by the total number of values across all groups.

Front

If a student scores 85% on a test worth 50% of their grade and 90% on a test worth 50%, what is their final grade?

Back

Final Grade = (85*0.5 + 90*0.5) = 87.5%.

Front

What is the impact of outliers on a weighted average?

Back

Outliers can significantly affect the weighted average, especially if they have a high weight, leading to a skewed representation of the data.

Front

How do you determine the necessary score on a final exam to achieve a desired average?

Back

Set up an equation using the weighted average formula, substituting known grades and weights, and solve for the unknown final exam score.