Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.4

Lesson 2.8Describe Data Using the Mean

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data.

Start hereWords for this lesson

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

WordWhat it meansExample
MeanSpanish: Media The average of a data set. Add all the values, then divide by how many values there are. Add, then divide by the count
AverageSpanish: Promedio Another word for the mean — the amount each value would be if the total were shared equally. A typical amount
Measure of centerSpanish: Medida de centro A single number used to describe the middle, or typical value, of a whole data set. Mean and median are both
Balance pointSpanish: Punto de equilibrio The value where the total distance of the data above it equals the total distance below it. The mean is the balance point. The mean balances the set
Data setSpanish: Conjunto de datos The whole collection of values that were gathered or measured. 8, 15, 11, 6
Target meanSpanish: Media objetivo The mean a person is trying to reach. A goal average of 29 points.

How it worksWorked examplefinding the mean of a data set

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

Five afternoons of dog walking earned 14, 21, 17, 19, and 24 dollars. Find the mean.

  1. Add every value. The five amounts give a total of 95 dollars.
  2. Count the values. There are five of them.
  3. Share the total evenly: divide it by the count of values.
  4. Check: the mean should land between the least and the greatest value.

Answer: The mean is 19 dollars — what each afternoon would earn if the money were shared evenly.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Five bowling scores are 46, 52, 38, 44, and 50. Find the mean score.

  1. Add every value: Total:
  2. How many values are there?
  3. Share the total evenly by dividing it by the count. Mean:
  4. Check: does your mean sit between the least and greatest value?
Answer:mean score

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The total of all the values is .
  • There are values, so I divided by .
  • The mean is , which means .
  • The mean must fall between and .

Word bank meanaveragetotalsumdividecountfair sharebalance pointcentertypicaldata setvalue

Watch outA common mistake

The most common mistake with the mean is adding correctly and then dividing by the wrong number — or not dividing at all. Students report the total (for 8, 10, 6, 12 they say the mean is 36) or they divide by a count that does not match the data, such as dividing a 4-value total by 5, or skipping a zero when counting the values. Before you finish, do two things: count the values in the data set out loud, and check that your mean lands between the smallest and largest value. A mean of 36 for data that never goes above 12 is impossible.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.4

Lesson 2.8Describe Data Using the Mean

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data.

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Put the steps for finding the mean in the correct order.

    Groups: Steps to find the mean (in order)
    • Step 1: Add every value in the data set to find the total
    • Step 2: Count how many values are in the data set
    • Step 3: Divide the total by the number of values
    • Step 4: Check that the answer lands between the smallest and largest value

    Hint Think about the counters: first you combine them all, and only then do you share them out.

Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Find the mean of: 4, 6, 8, 10

    1. A6
    2. B7
    3. C8
    4. D28

    Hint The mean is what each value would be if the total were shared out equally among all four numbers.

    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  2. 3Circle the letter of the best answer. Show how you know.

    Miguel earned $60 walking dogs over 4 days. What is his mean daily earning?

    1. A$4
    2. B$15
    3. C$20
    4. D$60

    Hint A typical day is the amount Miguel would earn if he earned the SAME amount all 4 days.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Find the mean of: 3, 5, 7, 9, 11

    1. A5
    2. B7
    3. C9
    4. D35

    Hint Mean means average: level all five numbers out so they are all the same.

    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  4. 5Circle the letter of the best answer. Show how you know.

    In her first 4 games, Sofia scored 12, 20, 16, and 11 points. What is her mean points per game so far?

    1. A14.75
    2. B15
    3. C20
    4. D59

    Hint The mean here answers: how many points per game has Sofia averaged so far?
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    The Mean Mistake (forgot to divide)

    1. 1Data setPoints scored in 4 games: 8, 10, 6, 12
    2. 2GoalFind the MEAN number of points per game.
    3. 3Add the values8 + 10 + 6 + 12 = 36
    4. 4AnswerMean = 36 points

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint The mean levels the total out across the games — a total by itself has not been leveled yet.

    Correct work
    Correct answer:

Explain your thinkingFour games are below 15 and four games are above 15. Does that already mean the data balances at 15? What else would you have to measure?

Sentence starter Counting games is not enough because ___. To balance, I have to measure how ___ each score is from ___, and then compare the total ___ to the total ___.

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.4

Lesson 2.8Describe Data Using the Mean

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the table.

    Data SetTotalHow Many ValuesMean
    6, 9, 12, 9
    20, 14, 16, 18, 22
    5, 8, 8, 11, 13, 15
    Show your work
  2. 2Mark and label each value on the number line.

    Data: 10, 12, 14, 16, 18. Place a marker at the mean of this data set.

    8101214161820
    Show your thinking
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    Sofia wants to average 15 points per game over 10 games. How many points does she need in all 10 games combined?

    1. A1.5 points
    2. B15 points
    3. C25 points
    4. D150 points
    per 1
  2. 4Circle the letter of the best answer. Show how you know.

    Sofia's points in games 1 through 9 were 12, 20, 16, 11, 17, 14, 15, 10, and 18. How many points has she scored so far?

    1. A15 points
    2. B123 points
    3. C133 points
    4. D150 points
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Sofia has 133 points after 9 games and needs 150 points in all to average 15 over 10 games. How many points must she score in game 10?

    1. A13 points
    2. B15 points
    3. C17 points
    4. D283 points
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    The Wrong Divisor

    1. 1Data setPoints in 4 games: 6, 11, 9, 14
    2. 2GoalFind the MEAN number of points per game.
    3. 3Add the values6 + 11 + 9 + 14 = 40
    4. 4DivideThe student divides by 5: 40 ÷ 5 = 8, so the mean is 8.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingFour games are below 15 and four games are above 15. Does that already mean the data balances at 15? What else would you have to measure?

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.4

Lesson 2.8Describe Data Using the Mean

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can determine the mean of a data set, use a target mean to find a missing value, and explain the mean as the fair share and the balance point of the data.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the table.

    GamePoints ScoredPoints Above or Below the Target Mean of 15
    Game 112
    Game 220
    Game 411
    Game 715
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A data set has a mean of 20. Every value in the data set is then increased by 4. What is the new mean?

    1. A5
    2. B20
    3. C24
    4. D80
    Put the data in order
    Work
Part 3Explain and correctreasoning
  1. 3Answer in complete sentences.

    Sofia realized she made an error: she actually scored 12 points in Game 8, not 10. Her other games are unchanged (12, 20, 16, 11, 17, 14, 15, and 18). How does this change the number of points she needs in Game 10 to average 15 points per game? Show how you know.

    Write your answer
  2. 4Find the mistake. Explain it, then show the correct work.

    The Missing Zero

    1. 1Data setGoals allowed in 4 games: 0, 3, 2, 7
    2. 2GoalFind the MEAN number of goals allowed per game.
    3. 3Add the values0 + 3 + 2 + 7 = 12
    4. 4DivideThe student says the shutout does not count as a game, so 12 ÷ 3 = 4 goals per game.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingFour games are below 15 and four games are above 15. Does that already mean the data balances at 15? What else would you have to measure?

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