Lesson 2.10Matching Center and Spread
Start hereWords, worked example, and sentence starters
Learning target I can choose the best measure of center for a data set based on its shape.
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. | One value far from the group |
| 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 examplematching the measures to the shape
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A symmetric set is 60, 62, 64, 66, 68. A second set is 60, 62, 64, 66, 210.
- Look at the shape first. The first set spreads evenly on both sides of its middle.
- For a symmetric set with no outlier, report the mean for center and the MAD for spread.
- The second set has an outlier, 210, sitting far above a tight group.
- For a skewed set, report the median for center and the IQR for spread.
Answer: Symmetric data pairs the mean with the MAD; data with an outlier pairs the median with the IQR.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Set A is 14, 16, 18, 20, 22. Set B is 14, 16, 18, 20, 175.
- Shape of Set A: Shape of Set B:
- Set A: report for center and for spread.
- Set B: report for center and for spread.
- Explain your choice for Set B:
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The shape of this set is because .
- For this shape I report for center.
- The matching measure of spread is .
- I avoided the here because .
Word bank symmetricskewedoutliermeanmedianMADinterquartile rangecenterspreadshapetypicalmatch
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 2.10Matching Center and Spread
Apply Day · Version ASupported practice
Learning target I can choose the best measure of center for a data set based on its shape.
-
1Complete each step, then write the final answer.
Which measure better shows a typical value for 5, 6, 7, 6, 30: the mean or the median?
Show your workHint Is one value far from the rest? An outlier pulls the mean toward it.
Final answer: -
2Complete each step, then write the final answer.
Which measure should you use for 2, 4, 6, 8, 10: the mean or the median?
Show your workHint Look for a value far from the rest. If there is none, use the mean.
Final answer: -
3Complete each step, then write the final answer.
Which measure better shows a typical value for 20, 22, 21, 23, 2: the mean or the median?
Show your workHint Is there an outlier? An outlier pulls the mean toward it.
Final answer:
Lesson 2.10Matching Center and Spread
Apply Day · Version BCore practice
Learning target I can choose the best measure of center for a data set based on its shape.
-
1Circle 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.
Show your work -
2Complete each step, then write the final answer.
Which measure better shows a typical value for 1.2, 1.5, 1.4, 1.3, 6.1: the mean or the median?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Which measure better shows a typical value for 12, 13, 14, 15, 51: the mean or the median?
Show your workFinal answer:
Lesson 2.10Matching Center and Spread
Apply Day · ChallengeExtension
Learning target I can choose the best measure of center for a data set based on its shape.
-
1Circle the letter of the best answer. Show how you know.
A data set of house prices contains one mansion worth far more than every other home. Which pair of measures best describes this data?
- AMedian and IQR
- BMean and MAD
- CMean and range
- DMode and range
Show your work -
2Circle the letter of the best answer. Show how you know.
Set P is 10, 20, 30, 40, 50. Set Q is 10, 12, 14, 16, 80. Which set needs the median to show a typical value?
- ASet P
- BSet Q
- CBoth sets
- DNeither set
Show your work -
3Complete each step, then write the final answer.
Which measure better shows a typical value for 40, 44, 42, 43, 41, 5: the mean or the median?
Show your workFinal answer: