Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6d

Lesson 2.10Matching Center and Spread

Start hereWords, worked example, and sentence starters

Name Date Period

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 example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Set C: 20, 22, 24, 26, 28. Set D: 20, 22, 24, 26, 150. Pick a pair for each.

C is symmetric: mean 24, MAD 12 ÷ 5 = 2.4.
D has an outlier (150): median 24, with the IQR.

Answer: C: mean and MAD. D: median and IQR.

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 out!A 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

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6d

Lesson 2.10Matching Center and Spread

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

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 work
Hint 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 work
Hint 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 work
Hint Is there an outlier? An outlier pulls the mean toward it.
Final answer:

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6d

Lesson 2.10Matching Center and Spread

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

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?
1. ANo. The outlier 32 pulls the mean up to 12. The median, 7, is better.
2. BYes. The mean uses every value, so it is always best.
3. 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 work
Final 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 work
Final answer:

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6d

Lesson 2.10Matching Center and Spread

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

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?
1. AMedian and IQR
2. BMean and MAD
3. CMean and range
4. 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?
1. ASet P
2. BSet Q
3. CBoth sets
4. 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 work
Final answer:

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help