Appropriate Measures
I can choose the best measure of center for a data set based on its shape.
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🎯 Content Objective / Objetivo de contenido
I can choose the best measure of center for a data set based on its shape.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
A top scorer's points were 22, 24, 20, 25, 23, 21, 58. The mean is 27.6 but the median is 23. Which should the league report as the 'typical' game, and why?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Stats Report Decision
The league is creating awards for the season. For the scoring title, they need to pick the best measure of a typical game. Here are the top scorer's points per game: 22, 24, 20, 25, 23, 21, 58. That 58-point game was a record-breaker! Should the league report the mean (27.6) or the median (23) as the player's typical scoring?
Concept Launch
💡 Should I use the mean or the median?
The mean and the median both describe the center of a data set, but one fits better depending on the shape. When the data has an outlier (a value far from the rest), the median is usually the better choice.
Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Mean Media |
The average. Add all the numbers, then divide by how many there are. El promedio. Suma todos los números y divide entre cuántos hay. |
Mean of 10, 20, 30 = (10+20+30) ÷ 3 = 20 | |
| Median Mediana |
The middle number when you put them in order. El número del medio cuando los pones en orden. |
Data: 5, 8, 12, 15, 20 → median is 12 (the 3rd of 5 values) | |
| Outlier Valor atípico |
A number that is much bigger or smaller than the rest. Un número mucho mayor o menor que los demás. |
Data: 12, 14, 13, 15, 45 → 45 is far from the cluster, so it is an outlier | |
| Skewed Sesgado |
When most data sits on one side with a tail on the other. Cuando la mayoría de los datos está de un lado con una cola del otro. |
Scores: 5, 6, 7, 8, 8, 35 → most scores are low, but 35 creates a tail to the right (skewed right) | |
| Data distribution Distribución de datos |
How the data looks: where it sits and how spread out it is. Cómo se ven los datos: dónde están y qué tan separados están. |
Symmetric = even on both sides. Skewed = bunched on one side with a tail | |
| Variability Variabilidad |
How spread out the numbers are. Qué tan separados están los números. |
88, 90, 89, 91 (low variability) vs. 50, 70, 95, 100 (high variability) |
Which Word Fits?
The average of a data set is the ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
A top scorer's points were 22, 24, 20, 25, 23, 21, 58. The mean is 27.6 but the median is 23. Which should the league report as the 'typical' game, and why?
👂 Listen For
Students choose the median (23) and identify 58 as an outlier that pulls the mean up to 27.6, making it unrepresentative.
Extend: Justify: by how much does removing the 58-point game change the mean? What does that show about outliers?
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Sort each sports data scenario into the correct category: Use Mean or Use Median.
✍️ Explore Discourse
What pattern do you notice about when median is the better choice?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
As you sort scenarios into 'Use Mean' or 'Use Median,' what clue tells you a data set needs the median instead of the mean?
👂 Listen For
A strong answer says the presence of an outlier or skew signals the median, while symmetric data with no outliers fits the mean.
Extend: Compare: give one sports example where the mean is the better choice and one where the median is. Justify each.
Practice Check A
A baseball player's batting averages over 6 seasons are: .280, .295, .290, .285, .300, .110. The .110 was an injury-shortened season. Which measure better represents the player's typical batting average?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A gymnast's scores are: 8.5, 8.8, 8.7, 8.6, 8.9. There are no outliers. Which measure best represents a typical score?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Statistical vs Not Sort
Drag each question into the correct column.
✍️ Justify Your Thinking
Sort each measure into whether it describes the CENTER of the data or the SPREAD of the data.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical." — and it works because ___.
Because Mean means ___, but a tricky part is ___, so I have to ___.
A common mistake with Mean is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Median to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical. because ___
Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical. but ___
Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Fill in the table using today's strategy.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A gymnast's scores are: 8.5, 8.8, 8.7, 8.6, 8.9. There are no outliers. Which measure best represents a typical score?
A baseball player's batting averages over 6 seasons are: .280, .295, .290, .285, .300, .110. The .110 was an injury-shortened season. Which measure better represents the player's typical batting average?
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A sports reporter writes: 'The average ticket price for the playoffs is $85.' The actual prices are: $45, $50, $48, $52, $55, $260. The $260 ticket is a courtside seat.
✍️ Connection Reasoning
Is $85 a fair way to describe a 'typical' ticket price? What measure should the reporter use?
The reporter used the ___, which is ___. A better measure would be the ___ (about ___) because ___. The courtside seat at $260 is an ___ that pulls the mean ___.
Turn & Talk — Connect
A reporter writes 'the average playoff ticket is $85,' but prices are $45, $50, $48, $52, $55, $260. Is $85 a fair 'typical' price? What measure should the reporter use?
👂 Listen For
Students explain $85 is misleading because the $260 courtside seat skews the mean upward, and the median (~$51) better reflects a typical ticket.
Extend: Critique: could the reporter be using the mean ON PURPOSE to make tickets sound pricier? Argue whether that is honest.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Data set: 15, 18, 16, 17, 15, 72. Which measure of center best represents the data?
Bonus Exit Check
A runner's mile times are: 7:10, 7:15, 7:12, 7:20, 12:00. The 12:00 was due to a cramp. Which measure best represents a typical mile?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students choose the median (23) and identify 58 as an outlier that pulls the mean up to 27.6, making it unrepresentative.
• A strong answer says the presence of an outlier or skew signals the median, while symmetric data with no outliers fits the mean.
• Students explain $85 is misleading because the $260 courtside seat skews the mean upward, and the median (~$51) better reflects a typical ticket.
• Students choose the median (~16.5), identify 72 as the outlier, and explain it would inflate the mean.
Common mistake: A common mistake in Appropriate Measures is skipping the key idea: "Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: Median, because the .110 outlier pulls the mean down — The .110 is an outlier that pulls the mean down to .260. The median (.2875) better represents typical performance because it isn't affected by the extreme value.
✓ Practice 2: Mean — The data is symmetric with no outliers, so the mean (8.7) best represents the typical score.
✓ Practice 3: Median — the outlier 12:00 pulls the mean too high — The 12:00 is an outlier that pulls the mean up. The median (7:15) better represents the runner's typical time.
✓ Practice 4: Median (7) — the outlier 50 inflates the mean — The mean (13.8) is higher than 5 of the 6 values because the outlier 50 pulls it up. The median (7) better represents a typical value.
✓ Exit ticket: Median, because 72 is an outlier — The value 72 is an outlier. The mean (25.5) is pulled high by 72 and doesn't represent the typical values. The median (16.5) is a better measure of center.