Unit 8 · Statistics & ProbabilityS1 · Averages · Telemetry

Mean, Median & Weighted Average

Turn centers into totals, handle frequency, and weight groups correctly.

28 min
Unlocks: Sensor Calibration

Ready when you are

7 steps · about 28 minutes

Start with the warm-up.

Start

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Warm-up

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Key terms

mean: Sum divided by number of values.
median: Middle value after sorting.
weighted average: A mean in which values contribute different counts or percentages.

Start by naming the quantity each problem asks for. That habit blocks the most common ACT trap.

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Try it first

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Take a calm first shot. Label what you know, write one relationship, and make the best choice you can.

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The big idea

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Build the picture before the arithmetic

Translate each group mean back into a total, combine totals, then divide by the combined count. For a missing value, target total minus known total is faster than trial and error.

Key idea

The decision that matters

Mean questions are often total questions in disguise: total = mean times count.

Mean

\bar{x}=\frac{\sum_{i=1}^{n}x_i}{n}

Write this relationship before inserting numbers. It keeps labels and units attached to the work.

A compact example

Five readings average 18, so their total is $5(18)=90$ . Adding a sixth reading of 24 gives a mean of $\frac{90+24}{6}=19$ .

Cue	Best move
Missing value	mean times count gives target total
Two groups	convert each group mean to a total

Trap

Averaging group averages without weighting

This error produces a believable answer. Pause before computing and say what each number means.

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Worked examples

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Skip check · 2 questions

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Worked example

Example 1: Recover a missing value

Problem

Five quiz scores have mean 84. Four scores are 78, 81, 86, and 90. Find the fifth score.

The target total is

5(84)=420

The four known scores total $78+81+86+90=335$ .

How should the missing score be recovered from the target mean?

The missing score is $420-335=85$ .

Why must the five quiz scores total 420?

Worked example

Example 2: Weight two groups

Problem

A class has 12 juniors averaging 76 and 18 seniors averaging 84. Find the class mean.

Junior total:

12(76)=912

. Senior total:

18(84)=1512

Combined total is $2424$ for $30$ students.

How should the two group means be combined?

The mean is $2424/30=80.8$ .

Why must each class mean be weighted by its group size?

Faded example · you finish it

Example 3: You finish it

Problem

The sorted data are 3, 7, 8, 12, 15, 19. Find the median.

Sort first; with an even count, average the two middle values.

Which completion is correct?

Which reason validates the result?

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Practice

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Spot the mistake

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Spot the mistake

Where did it go wrong?

One line has an error. Click the line where it first goes wrong.

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Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36

These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.