Describe the Data Using the Median
I can find the median of a data set and use it to describe what is typical.
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🎯 Content Objective / Objetivo de contenido
I can find the median of a data set and use it to describe what is typical.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The team scored 42, 38, 55, 41, 38, 44, 40 points over 7 games. Which 'average' would best tell the coach the team's typical scoring: mean, median, or mode?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Game Day Stats
You're the stats analyst for the school basketball team. Coach needs a report on the team's scoring: in the last 7 games they scored 42, 38, 55, 41, 38, 44, and 40 points. Which average best represents the team's typical performance?
Concept Launch
💡 What are mean, median, and mode?
Mean, median, and mode are three ways to find the center, or "typical" value, of a data set. The mean is the average, the median is the middle, and the mode is the most common value.
Measures of Center: Median. Formula: Median = Middle value in an ordered set. 1. Order all data values from least to greatest. 2. Odd count: The median is the exact center number. 3. Even count: The median is the mean of the two middle numbers
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Describe the Data Using the Median Describir los datos con la mediana |
Using the middle value of the ordered data to say what is typical for the whole set. Usar el valor del medio de los datos ordenados para decir qué es típico en todo el conjunto. |
2, 4, 4, 6, 9 → median 4 | |
| Median Mediana |
The middle number when you put them in order. El número del medio cuando los pones en orden. |
Data: 1, 3, 5, 7, 9 → the middle (3rd) value is 5, so median = 5 | |
| Mode Moda |
The number that shows up most often. El número que aparece más veces. |
Data: 2, 3, 3, 5, 7 → 3 appears twice (most often), so mode = 3 | |
| Outlier Valor atípico |
A number that is much bigger or smaller than the rest. Un número mucho mayor o menor que los demás. |
Data: 10, 12, 11, 13, 50 → 50 is far from the others, so 50 is an outlier | |
| 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. |
If most values cluster in the center with fewer at the ends, the distribution is symmetric | |
| Variability Variabilidad |
How spread out the numbers are. Qué tan separados están los números. |
8, 9, 10, 11 has low variability (close together); 2, 10, 25, 40 has high variability (far apart) |
Which Word Fits?
When one value sits far from the rest, describe the typical value with 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
The team scored 42, 38, 55, 41, 38, 44, 40 points over 7 games. Which 'average' would best tell the coach the team's typical scoring: mean, median, or mode?
👂 Listen For
Students distinguish the three measures and justify a choice, noting the mode (38) is the most repeated and the mean/median sit near the center.
Extend: Justify: which measure would change the most if one game's 55 were actually 100? Explain why.
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
Basketball scores this month: 38, 38, 41, 45, 53. Order the scores on the number line, then find the mean, median, and mode. Place markers at: A = Mean, B = Median, C = Mode.
✍️ Explore Discourse
The mean (43) is higher than the median (41). Why? Which better represents a typical game?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
After ordering the scores on the number line, how do you find the median, and how is it different from the mean you calculated?
👂 Listen For
A strong answer orders the data, finds the middle value as the median, and explains the mean is found by summing all values and dividing.
Extend: Compute and compare: find the mean and median of 42, 38, 55, 41, 38, 44, 40. Are they close? What does that tell you?
Practice Check A
Data set: 4, 6, 6, 8, 10, 12. What is the median?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Find the mean of: 10, 14, 8, 12, 16
✍️ 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 step into the correct order for finding the median.
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: "Measures of Center: Median. Formula: Median = Middle value in an ordered set. 1. Order all data values from least to greatest. 2. Odd count: The median is the exact center number. 3. Even count: The median is the mean of the two middle numbers" — and it works because ___.
Because Describe the Data Using the Median means ___, but a tricky part is ___, so I have to ___.
A common mistake with Describe the Data Using the Median 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
Measures of Center: Median. Formula: Median = Middle value in an ordered set. 1. Order all data values from least to greatest. 2. Odd count: The median is the exact center number. 3. Even count: The median is the mean of the two middle numbers because ___
Measures of Center: Median. Formula: Median = Middle value in an ordered set. 1. Order all data values from least to greatest. 2. Odd count: The median is the exact center number. 3. Even count: The median is the mean of the two middle numbers but ___
Measures of Center: Median. Formula: Median = Middle value in an ordered set. 1. Order all data values from least to greatest. 2. Odd count: The median is the exact center number. 3. Even count: The median is the mean of the two middle numbers 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.
Find the mean of: 10, 14, 8, 12, 16
Core practice aligned to the standard.
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
Your class took a math quiz. The scores were: 85, 92, 78, 88, 92, 95, 72, 88, 92, 84. The teacher says 'most students scored around 87.' A student disagrees and says 'the most common score was 92.'
✍️ Connection Reasoning
Who is using the mean, and who is using the mode? Which is more useful here?
The teacher used the ___ (about 86.6). The student used the ___ (92). The ___ is more useful here because ___.
Turn & Talk — Connect
Quiz scores were 85, 92, 78, 88, 92, 95, 72, 88, 92, 84. The teacher says 'most scored around 87'; a student says 'the most common score was 92.' Who used the mean, and who used the mode?
👂 Listen For
Students identify 87 as the mean and 92 as the mode, and argue which is more useful for describing the class's typical performance.
Extend: Critique: is the student technically right that 92 was 'the most common,' yet possibly misleading about how the class did? Defend.
Summarize: Describe the Data Using the Median
Measures of Center: Median. Formula: Median = Middle value in an ordered set. 1. Order all data values from least to greatest. 2. Odd count: The median is the exact center number. 3. Even count: The median is the mean of the two middle numbers
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Data set: 4, 7, 10, 7, 12. What is the median, and what does it tell you?
Bonus Exit Check
Find the median of: 3, 7, 2, 9, 5
✍️ 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 distinguish the three measures and justify a choice, noting the mode (38) is the most repeated and the mean/median sit near the center.
• A strong answer orders the data, finds the middle value as the median, and explains the mean is found by summing all values and dividing.
• Students identify 87 as the mean and 92 as the mode, and argue which is more useful for describing the class's typical performance.
• Students order to 4, 7, 7, 10, 12 and identify 7 as the median (middle value).
Common mistake: A common mistake in Mean, Median, and Mode is finding the median without ordering the data first — students pick the middle number straight from the list as given (for 9, 4, 7, 2, 6 they say the median is 7, the middle position in that original order) instead of sorting least to greatest (2, 4, 6, 7, 9) and finding the true middle value, 6. Before finalizing a median, always reorder the data smallest to largest, then count to the middle position — and if there is an even number of values, average the two middle numbers.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 7 — With 6 values, the median is the average of the 3rd and 4th values: (6 + 8) ÷ 2 = 7.
✓ Practice 2: 12 — Sum = 10 + 14 + 8 + 12 + 16 = 60. Mean = 60 ÷ 5 = 12.
✓ Practice 3: 5 — Ordered: 2, 3, 5, 7, 9. The middle value is 5.
✓ Practice 4: 4 — 4 appears three times — more than any other value. Mode = 4.
✓ Exit ticket: 7 — a typical value in this set is about 7 — Put the values in order first: 4, 7, 7, 10, 12. With five values the middle is the 3rd, so the median is 7 — half the values sit at or below it.