Weighted Averages of Points Practice Quiz (12 questions)

Explanation

A midpoint is the exact middle of a line segment. An endpoint is at the segment’s edge, a weighted mean is a different kind of average, and a ratio compares quantities.

Explanation

A weighted average assigns different levels of importance, or weights, to values. A midpoint is the exact center of a segment, an ordinary average treats values without differentiated weights, and a ratio compares quantities.

Explanation

The average of two numbers is their sum divided by 2, so $\frac{72+88}{2}=\frac{160}{2}=80$. The value 160 omits division, dividing by 1 uses the wrong denominator, and 8 comes from half the difference.

Explanation

The simple average is the sum divided by 2: $\frac{76+92}{2}=\frac{168}{2}=84$, the number-line midpoint. Choosing 76 or 92 confuses the average with an endpoint, while 8 is half the difference.

Explanation

Multiply each value by its weight and add: $0.6(70)+0.4(95)=42+38=80$. The simple average gives 82.5, while reversing the weights gives 85.

Explanation

The weighted average is $0.80(80)+0.20(90)=64+18=82$. The value 85 is the simple average, while 88 results from swapping the weights.

Explanation

A weighted average lies proportionally closer to the value with the greater weight. A midpoint is equidistant from both values, and a weighted average of two values does not lie outside their interval.

Explanation

The distances are $82-80=2$ and $90-82=8$, so their ratio is $2:8=1:4$. The heavier weight corresponds to the shorter distance, so reversing the ratio or matching it directly to the weight ratio gives the wrong result.

Explanation

With weights 1:2, the weighted average is $\frac{1}{3}(3)+\frac{2}{3}(9)=1+6=7$. The value 5 comes from the original 2:1 ratio, while 6 is the midpoint.

Explanation

A weighted average is found by determining the weights, finding their total, multiplying each value by its own weight, and adding the weighted values. The arithmetic mean ignores weights, while the other methods misuse the individual and total weights.

Explanation

The ratio totals $1+3+2+4=10$ parts, so the 2-part ingredient has normalized weight $\frac{2}{10}$. Using 2 or 4 as the denominator confuses an individual part count with the total; $\frac{3}{10}$ is the weight for the 3-part ingredient.

Explanation

Multiply each grade by its weight and add: $92.5(0.10)+92.5(0.20)+90(0.30)+80(0.40)=86.75$. Equal weighting gives 88.75%, while misassigning the test and final weights gives 85.50%.