Statistics and Probability · 35 minutes
Suggested grades 10–12 · Unit 1: Distributions and paired-data models · Lesson 1 of 2
Choose Center and Spread for Two Distributions
Compare summaries while explaining what an extreme value changes and what it hides.
Mr. S Teaches · Original starter lesson · HS-STAT-01 · Grade range is planning guidance.Watch, notice, discuss
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Mean and standard deviation versus median and IQR | AP Statistics | Khan Academy
By Khan Academy
Compare measures suited to symmetric and skewed data, then justify the lesson’s comparison.
Open on YouTube: Mean and standard deviation versus median and IQR | AP Statistics | Khan Academy (opens a new tab) ↗The Effects of Outliers on Spread and Centre (1.5)
By Simple Learning Pro
Observe which center and spread measures are sensitive to extreme observations.
Open on YouTube: The Effects of Outliers on Spread and Centre (1.5) (opens a new tab) ↗Which center and spread describe these distributions fairly, and how does an outlier change that choice?
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Learning objective
Calculate means, medians and interquartile ranges and justify a comparison in context.
Before you begin
- Mean and median
- Ordered data
Gather your materials
- Paper and pencil
- Graph paper
- Calculator for checking results
Language to know
- median
- The middle value of ordered data, or the mean of the middle pair.
- interquartile range
- The difference Q3−Q1, describing the middle half’s spread.
- skew
- An asymmetry in a distribution’s shape.
Understand the concept
Fictional completion times in minutes are A:2,3,4,5,6,7,8 and B:2,3,4,5,6,7,29. An unusually long time pulls the mean more than the median. The interquartile range summarizes the middle half, so it can miss an extreme tail. Here use quartiles as the medians of the lower and upper halves after excluding an odd sample’s overall median.
Teach it step by step
- Plot both ordered lists on one number-line scale, retaining the point 29.
- Calculate each mean and median and describe the right tail in B.
- Using the stated quartile convention, find Q1,Q3 and IQR for each.
- Write a comparison explaining why equal medians and IQRs do not mean identical distributions.
Make the thinking visible
Worked example or model response
A has mean 5, median 5, Q1=3,Q3=7,IQR 4. B has mean 8, median 5 and the same IQR 4. Its 29-minute observation creates a longer right tail; the median/IQR pair describes the center without revealing the entire range.
Guided practice
Compare means and medians for 3,4,5,6,7 versus 3,4,5,6,22.
Independent practice
1. Find median and IQR of 1,2,3,4,5 using the stated convention. 2. Explain why reporting only an IQR may hide an unusually high value.
Quick assessment
Why is deleting 29 merely because it is unusual not a justified cleaning decision?
Answer key & assessment criteria
Answers and teaching guidance
- Guided: Means 5 and 8; both medians 5. The high observation changes the mean while leaving the median unchanged.
- Independent 1: Median 3,Q1=1.5,Q3=4.5,IQR 3. 2: IQR covers the middle half, not every observation.
- Quick check: An unusual value may be valid; investigate its origin and report a justified treatment rather than removing inconvenient evidence.
Look for: Require the learner to explain the interpretation and check, not only state a result. Distinguish an exact value from a rounded approximation and attend to the stated domain.
Make it work for your learner
More support
Use sorted value cards and a shared dot-plot scale before calculating.
Extension challenge
Create two data sets with equal means but very different medians or spreads.
Verified references · Selected contributions
Standards connections
Subject-content standards
These records identify the part of a subject standard practiced here. Course placement is instructional guidance; the source’s category or band remains authoritative.
Contributes to Common Core standard
HSS.ID.A.2
Common Core · High school · Statistics and Probability
Regular high school mathematics standard
Compare suitable measures of center and spread across distributions.
Read the official standard ↗This lesson contributes selected skills; broader applications and full standard coverage require further instruction.
Verified 2026-11-04. Selected contribution, not full attainment.
Contributes to Common Core standard
HSS.ID.A.3
Common Core · High school · Statistics and Probability
Regular high school mathematics standard
Explain an extreme value’s effects in the data context.
Read the official standard ↗This lesson contributes selected skills; broader applications and full standard coverage require further instruction.
Verified 2026-11-04. Selected contribution, not full attainment.