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

Lesson 2.102.10 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
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?

  1. Order the values and look for one far from the rest: 72 sits alone above the group.
  2. Find the median: the middle of the seven ordered ages is 12.
  3. Find the mean: the ages total 140, and sharing that among seven gives 20.
  4. 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?

  1. Order the values and circle any value far from the rest:
  2. Median:
  3. Total: Mean:
  4. Which measure sits closer to most of the values? Why?
Answer:better measure of center, with a reason

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.

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

Lesson 2.102.10 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    0246810121416Muffins sold
    One low day sits far from the others.

    A café sold 12, 14, 13, 15, 14 and 0 muffins on 6 days. It was closed one day. Which measure better shows a typical day?

    1. 1Which value is the outlier?
    2. 2The total is 68. Find the mean to the nearest tenth.
    3. 3Put the values in order. What is the median?
    4. 4Which measure better shows a typical day?
    Final answer:
  2. 2Complete each step, then write the final answer.
    5791113151719212325Prices in dollars
    The platter is far from the other prices.

    Sandwiches cost $6, $7, $8, $7 and $7. Then a $25 platter is added to the menu. Which measure changes more: the mean or the median?

    1. 1Find the mean and the median before the platter.
    2. 2Find the mean and the median after the platter.
    3. 3Which measure moved?
    4. 4Why does the median stay at 7?
    Final answer:
  3. 3Complete 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:
  4. 4Complete each step, then write the final answer.

    A theater sold 48, 52, 50, 49 and 51 tickets on 5 nights. Which measure should you use for a typical night: the mean or the median?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A soccer team scored 3, 4, 2, 3, 4, 3 and 18 goals in 7 games. The coach wants one number for a typical game. What number should the coach report?

    Show your work
    Final answer:
  6. 6Circle 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

Explain your thinkingCan an outlier pull the mean down as well as up? Use the muffin data and the platter data to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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