Weighted Averages of Points

From the study guide

Course Outline

  1. Averages, Midpoints, and Ratios
  2. Calculating a Simple Average
  3. Weighted Averages of Two Points
  4. How Changing Weights Moves Points
  5. Weighted Averages of Multiple Points
  6. Composite Scores and Grade Examples

1. Averages, Midpoints, and Ratios

Key Concepts & Definitions

  • Midpoint: The exact middle of a line segment.
  • Weighted average: A type of mean calculated by assigning different levels of importance, or weights, to a set of values.
  • Average: The total of all values divided by the number of values.
  • Ratio: A mathematical comparison of two quantities.

Memory Hook

An average combines values; a midpoint marks the exact center of a segment.

2. Calculating a Simple Average

★ Must-know

📐 Formula - The average of two numbers is first number+second number2\frac{\text{first number} + \text{second number}}{2}.

Further detail

  • The average of 80 and 90 is 80+902=85\frac{80+90}{2}=85, which is also the midpoint between 80 and 90 on a number line.

3. Weighted Averages of Two Points

📐 Formula - A weighted average is the sum of each value multiplied by its weight: Weighted average=w1x1+w2x2\text{Weighted average}=w_1x_1+w_2x_2.

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Practice quiz preview

1. What does the midpoint of a line segment represent?

2. Two values contribute to a mean, but the first value is assigned greater importance than the second. Which kind of mean is being used?

3. A student finds the average of 72 and 88. Which calculation gives the correct average?

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Flashcard preview

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?

first number+second number2\frac{\text{first number} + \text{second number}}{2}

How is the weighted average of values x1x_1 and x2x_2 calculated using weights w1w_1 and w2w_2?

w1x1+w2x2w_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.

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Frequently asked questions

What does the Weighted Averages of Points study guide cover?

It covers the core concepts of Weighted Averages of Points, organized by topic with the key definitions, explanations and takeaways, so it's easier to learn and remember.

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How many questions are in the Weighted Averages of Points quiz?

The practice quiz has 12 multiple-choice questions, each with an explanation. Use it to check what you know and find your gaps.

Take the quiz (12 questions) →

How do I study Weighted Averages of Points with flashcards?

There are 23 flashcards on Weighted Averages of Points, with a question on the front and the answer on the back. Try to recall each answer before you flip, and let spaced repetition bring back the ones you miss.

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