Weighted Averages of Points Flashcards (23 cards)

What is the midpoint of a line segment?

Its exact middle.

How does a weighted average account for values?

It assigns different levels of importance, or weights, to the values.

What is the formula for the average of two numbers?

$\frac{\text{first number} + \text{second number}}{2}$

How is the weighted average of values $x_1$ and $x_2$ calculated using weights $w_1$ and $w_2$?

$w_1x_1+w_2x_2$

What is the weighted average of a daily grade of 80 weighted at 80% and an exam grade of 90 weighted at 20%?

82

Toward which value does a weighted average lie proportionally closer?

The value with the greater weight.

How do you calculate a weighted average from multiple values and weights?

Multiply each value by its weight, then add the weighted values.

How is an average calculated?

Divide the total of all values by the number of values.

What does a ratio compare?

Two quantities.

What is the average of 80 and 90?

85.

Where is the average of 80 and 90 located on a number line?

At the midpoint between 80 and 90.

What is the weighted average of 5 and 13 with weights in the ratio 2:3?

9.8

For points 80 and 90 weighted 80% and 20%, what is the ratio of distances from their average?

1:4.

For points 80 and 90 with weighted average 82, which point has the shorter distance to the average?

80.

For points 3 and 9 weighted in the ratio 2:1, what is the weighted average?

5.

For points 3 and 9 weighted in the ratio 1:2, what is the weighted average?

7.

For points 3 and 9 weighted in the ratio 1:3, what is the weighted average?

7.5.

For points 3 and 9, changing the weight ratio from 1:2 to 1:3 moves the average toward which point?

9.

How many total parts are in the ratio 1:3:2:4?

10 parts.

What normalized weights correspond to the ratio 1:3:2:4?

$\frac{1}{10}, \frac{3}{10}, \frac{2}{10}, \frac{4}{10}$.

What is the weighted cost of the coffee blend with Bean A at $10, Bean B at $20, and a 1:3 ratio?

$17.50 per pound.

What is the gaming score weighted from 1,000 points at 50%, 1,500 at 30%, and 800 at 20%?

1,110 points.

What weighted average results from the stated grade example?

86.75%.