Lesson 2.102.10 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can choose the best measure of center for a data set based on its shape — one step at a time, with support.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| MeanSpanish: Media | The average. Add all the numbers, then divide by how many there are. | Mean of 10, 20, 30 = (10+20+30) ÷ 3 = 20 |
| MedianSpanish: Mediana | The middle number when you put them in order. | Data: 5, 8, 12, 15, 20 → median is 12 (the 3rd of 5 values) |
| OutlierSpanish: Valor atípico | A number that is much bigger or smaller than the rest. | 2, 3, 4, 32 → 32 |
| SkewedSpanish: Sesgado | When most data sits on one side with a tail on the other. | A long tail to the right |
| Data distributionSpanish: Distribución de datos | How the data looks: where it sits and how spread out it is. | Symmetric = even on both sides. Skewed = bunched on one side with a tail |
| VariabilitySpanish: Variabilidad | How spread out the numbers are. | 88, 90, 89, 91 (low variability) vs. 50, 70, 95, 100 (high variability) |
How it worksWorked examplechoosing between the mean and the median
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Seven ages at a family party are 8, 9, 11, 12, 13, 15, 72. Which center describes them better?
- Order the values and look for one far from the rest: 72 sits alone above the group.
- Find the median: the middle of the seven ordered ages is 12.
- Find the mean: the ages total 140, and sharing that among seven gives 20.
- The mean now sits above all but one age, so the outlier pulled it away from the group.
Answer: The median, 12, describes a typical age better, because the outlier 72 skews the mean.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Seven weekly tips in dollars are 24, 26, 28, 30, 32, 34, 176. Which center fits better?
- Order the values and circle any value far from the rest:
- Median:
- Total: Mean:
- Which measure sits closer to most of the values? Why?
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The outlier in this set is because .
- The median is and the mean is .
- The mean is pulled because .
- I would report the because .
Word bank outlierskewedclustergapmedianmeantypicalcenterpulledsymmetricdescribedata set
Watch outA common mistake
A common mistake in Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present. For example, given a player's points per game 14, 16, 15, 17, 16, 58, a student calculates the mean (136 ÷ 6 ≈ 22.7) and reports that as the typical game — but 58 is far from the cluster of 14–17, so it pulls the mean above 5 of the 6 games. The median (16) actually represents a typical game here. Before choosing a measure, always scan the data for an outlier or a long tail first: only use the mean once you've confirmed the data has neither.
Lesson 2.102.10 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can choose the best measure of center for a data set based on its shape — one step at a time, with support.
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1Complete each step, then write the final answer.
Four amounts are close together. 42 is far away. Five friends spent $8, $10, $9, $11 and $42 at a fair. Which measure better shows a typical amount: the mean or the median?
- 1Which value is far from the rest?
- 2The total is $80. Find the mean. Is it more than most values?
- 3Put the values in order. What is the median?
- 4Which measure better shows a typical amount?
Final answer: -
2Complete each step, then write the final answer.
No value is far from the rest. Lily ran 3, 5, 4, 6 and 2 miles this week. Which measure should we use for a typical run: the mean or the median?
- 1Is any value far from the rest?
- 2There is no outlier. Which measure should we use?
- 3The total is 20. What is the mean?
Final answer: -
3Complete each step, then write the final answer.
Which measure better shows a typical value for 2, 3, 3, 4, 28: the mean or the median?
Show your workHint Look for a value far from the rest. Does it pull the mean up?
Final answer: -
4Complete each step, then write the final answer.
A player scored 18, 21, 19, 20, 22 and 20 points in 6 games. Which measure should you use for a typical game: the mean or the median?
Show your workHint Is any score far from the others? If not, the mean can use every score.
Final answer: -
5Complete each step, then write the final answer.
Test scores in a small class are 85, 90, 88, 92 and 40. One student was sick. Which measure better shows a typical score: the mean or the median?
Show your workHint 40 is far from the other scores. Does it pull the mean up or down?
Final answer: -
6Circle the letter of the best answer. Show how you know.
Sam says the mean is always the best typical value because it uses every number. The data are 6, 7, 7, 8, 32. Is Sam right?
- ANo. The outlier 32 pulls the mean up to 12. The median, 7, is better.
- BYes. The mean uses every value, so it is always best.
- CYes. The mean, 12, is close to most values.
Hint Find the mean. Is it close to most of the values?
Show your work
Explain your thinkingWhen is the mean a good choice? When is the median better? Use Lily's miles and the fair data to explain.
Sentence starter I use the mean when ___. · I use the median when ___ because ___.