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

Lesson 2.82.8 Small Group · Group 2

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, 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 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 2.82.8 Small Group · Group 2

Group 2Challenge 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, 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.
    Target: 5 games88888? points
    5 games, each with a fair share of 8 points.

    Marco wants a mean of 8 points over 5 games. He scored 6, 9, 7 and 5 points in games 1 to 4. How many points does he need in game 5?

    1. 1Multiply the target mean by the number of games. What is the target total?
    2. 2What is the total of games 1 to 4?
    3. 3Subtract. How many points does Marco need in game 5?
    Final answer:
  2. 2Complete each step, then write the final answer.
    34567891011121314meanData values
    Three known values. The mean is the balance point.

    The mean of four numbers is 9. Three of them are 4, 11 and 13. Find the fourth number. Then check the balance.

    1. 1What must the four numbers add to?
    2. 2What is the fourth number?
    3. 3Add the distances on each side of 9.
    4. 4Why must the distances on each side of the mean be equal?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the mean of 2.5, 4, 6.5 and 3.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Dev wants a mean of 85 on 4 tests. His first 3 scores are 80, 88 and 79. What must he score on test 4?

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

    A class collected cans for 5 days. The mean was 24 cans per day. How many cans did the class collect in all?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    The mean of 6, 10 and 14 is 10. A new value, 2, is added. Nina says the mean stays 10. What is the new mean?

    Show your work
    Final answer:

Explain your thinkingA value equal to the mean is added to a data set. Does the mean change? Use the balance point to defend your answer.

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