Unit 8 · Standard 6.SP.5d
Appropriate Measures
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Mean of 10, 20, 30 = (10+20+30) ÷ 3 = 20
Mean
The average. Add all the numbers, then divide by how many there are.
Data: 5, 8, 12, 15, 20 → median is 12 (the 3rd of 5 values)
Median
The middle number when you put them in order.
Data: 12, 14, 13, 15, 45 → 45 is far from the cluster, so it is an outlier
Outlier
A number that is much bigger or smaller than the rest.
Scores: 5, 6, 7, 8, 8, 35 → most scores are low, but 35 creates a tail to the right (skewed right)
Skewed
When most data sits on one side with a tail on the other.
Symmetric = even on both sides. Skewed = bunched on one side with a tail
Data distribution
How the data looks: where it sits and how spread out it is.
88, 90, 89, 91 (low variability) vs. 50, 70, 95, 100 (high variability)
Variability
How spread out the numbers are.
Key Ideas & Notes
- 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!
Think About It
- How does the 58-point game compare to the other scores?
- What is the mean? What is the median?
- Which measure is closer to what this player usually scores?
My Notes
Guided Examples
Example 1
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?
Solution: The data is symmetric with no outliers, so the mean (8.7) best represents the typical score.
Answer: A. Mean
Example 2
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?
Solution: The 12:00 is an outlier that pulls the mean up. The median (7:15) better represents the runner's typical time.
Answer: A. Median — the outlier 12:00 pulls the mean too high
Example 3
Data set: 5, 6, 7, 7, 8, 50. The mean is about 13.8 and the median is 7. Which better represents the typical value?
Solution: 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.
Answer: A. Median (7) — the outlier 50 inflates the mean
Write About the Math The Writing Revolution
I can explain my choice using the words mean, median, outlier, and skewed.
1. Kernel Sentence subject + verb
Model: Mean is the average. Add all the numbers, then divide by how many there are.Media es el promedio. Suma todos los números y divide entre cuántos hay.
Write a kernel sentence about mean. Use a subject and a verb.Escribe una oración base sobre media. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Mean matters in mathMedia importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Mean matters in math because ___.Media importa en matemáticas porque ___.
Mean matters in math, but ___.Media importa en matemáticas, pero ___.
Mean matters in math, so ___.Media importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about mean.Di un hecho verdadero sobre mean.
Mean ___.
Ask a question about mean.Haz una pregunta sobre mean.
How does ___ ?¿Cómo ___ ?
Show excitement about mean.Muestra entusiasmo sobre mean.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with mean.Dile a un compañero qué hacer con mean.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I chose the ___ because ___.Elegí la ___ porque ___.
It fits the data because ___.Encaja con los datos porque ___.
An average can mislead when ___.Un promedio puede engañar cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. 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?
- Median, because the .110 outlier pulls the mean down
- Mean, because it uses all the data
- Mean, because .110 is a real season
- Neither measure works
2. Match the reason with whether to use mean or median.
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A local newspaper reports that the average home price in a neighborhood is $450,000. The actual prices are: $180K, $200K, $190K, $210K, $195K, $1,725K. Is the reporter's claim misleading? Calculate the mean and median and explain which better represents a 'typical' home price.
Sentence starter: Mean = ___. Median = ___. The reporter's claim is ___ because the outlier ($1,725K) pulls the mean ___. The ___ (about $___) better represents a typical home price because ___.
Reflect — Exit Ticket
Data set: 15, 18, 16, 17, 15, 72. Which measure of center best represents the data?
- Median, because 72 is an outlier
- Mean, because it uses all values
- Mean, because it is always best
- Neither works for this data
Answer Key & Teacher Guide
- Try It 1: A. 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.
- Try It 2:
- Exit Ticket: A. 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.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Mean is the average. Add all the numbers, then divide by how many there are.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).