Part 1 — A Surprising Average

Priya collected the prices of 5 backpacks for a review: 10, 12, 11, 13, 54. The mean came out high. "Something's pulling the average up," she said — an outlier.

Mean = (10 + 12 + 11 + 13 + 54) ÷ 5 = 100 ÷ 5 = $20. But four of the five prices are near $11–$13. The $54 outlier pulls the mean far above a "typical" price.

Analyze — Q1

Why is the mean of $20 misleading for these backpacks?

Solve It — #1

Find the mean of 3, 4, 5, 6, 7.

Mean:

Part 2 — A Better Center

"When there's an outlier, the median often describes the data better," Priya explained. She ordered the prices and found the middle: 10, 11, 12, 13, 54.

In order, the middle of five values is the 3rd: $12. The median ($12) is much closer to a typical backpack than the mean ($20).

Solve It — #2

Find the median of 8, 2, 9, 4, 100. (Order first!)

Median:

Analyze — Q2

Why is the median less affected by an outlier than the mean?

Part 3 — Measuring Spread (MAD)

For consistency, Priya used the mean absolute deviation (MAD) — the average distance of each value from the mean. For 1, 3, 5, 7, the mean is 4.

Distances from 4: |1−4|=3, |3−4|=1, |5−4|=1, |7−4|=3. MAD = (3 + 1 + 1 + 3) ÷ 4 = 8 ÷ 4 = 2.

Solve It — #3

Find the MAD of 2, 4, 6, 8. (Mean is 5. Average the distances from 5.)

MAD:

Part 4 — Comparing Two Teams

Two quiz teams both averaged 15 points. But were they equally consistent? Priya compared the range of each. Team Falcon scored 12, 15, 9, 20.

Falcon range = 20 − 9 = 11. A larger range means scores are more spread out (less consistent); a smaller range means more consistent.

Solve It — #4

Team Hawk scored 14, 16, 13, 17. Find Hawk's range.

Range:

Analyze — Q3

Two teams have the same mean. What does a smaller range tell you?

After You Read — Analytical Writing

Make a Mathematical Argument

Choose one prompt. Write a clear paragraph (5–7 sentences) using numbers from the story as evidence.

Prompt A — Choose the best measure. For the backpack prices, argue whether the mean ($20) or the median ($12) better describes a typical price. Use the data and the outlier as evidence.

Prompt B — Judge consistency. Falcon and Hawk have the same mean. Use range (and the idea of MAD) to argue which team is more consistent, citing the actual numbers.

Optional academic frame: "The data shows ______; therefore the better measure/team is ______ because ______."

Write your argument here (included when you print or download):

Challenge Extension

Think Further

Priya removes the $54 outlier from 10, 12, 11, 13, 54. What is the new mean of the remaining four prices, and how much did removing one value change the mean? Explain what this shows about outliers. (Try it, then check with your teacher.)

How You Are Scored

Rubric

Category	4 — Advanced	3 — Proficient	2 — Developing
Comprehension & inference	All analysis questions correct; explains outlier & spread reasoning	2 of 3 correct	1 correct
Multi-step math	All 4 Solve-It answers correct (mean, median, MAD, range)	3 correct	2 correct
Mathematical argument	Clear claim; chooses the right measure with numeric evidence	Claim with some evidence	States a claim with little evidence