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

Lesson 2.3Describe the Data Using the Median

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the median of a data set and use it to describe what is typical.

Start hereWords for this lesson

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

WordWhat it meansExample
MedianSpanish: Mediana The middle number when you put them in order. 2, 6, 9 . . . median is 6
ModeSpanish: Moda The number that shows up most often. Data: 2, 3, 3, 5, 7 → 3 appears twice (most often), so mode = 3
OutlierSpanish: Valor atípico A number that is much bigger or smaller than the rest. 2, 3, 4, 40 → 40
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. If most values cluster in the center with fewer at the ends, the distribution is symmetric
VariabilitySpanish: Variabilidad How spread out the numbers are. 8, 9, 10, 11 has low variability (close together); 2, 10, 25, 40 has high variability (far apart)
Measure of centerSpanish: Medida de tendencia central One number that describes a typical value in a data set. The median is one of them

How it worksWorked examplefinding the median of an odd-sized set

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

Seven bowling scores are 96, 88, 104, 91, 99, 86, 93. What is the median score?

  1. Write the values in order, crossing each one off the original list as you place it.
  2. Ordered: 86, 88, 91, 93, 96, 99, 104.
  3. Count them. Seven values is an odd count, so one value sits exactly in the middle.
  4. Cross off one from each end until a single value is left.

Answer: The median score is 93, the middle value of the ordered list.

Now you trySame steps, your turn

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

Seven snack prices in cents are 65, 72, 58, 81, 69, 77, 62. What is the median price?

  1. Write the values in order from least to greatest:
  2. How many values are there? Is that count odd or even?
  3. Cross off one value from each end until only one remains in the middle.
  4. The median is cents.
Answer:median price in cents

Say it and write itSentence starters

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

  • In order, the values are .
  • There are values, so the middle one is in position .
  • The median is , which means .
  • About half the values are below .

Word bank medianorderleastgreatestmiddlehalftypicalcenterpositioncountoutlierdata

Watch outA common mistake

A common mistake in Mean, Median, and Mode is finding the median without ordering the data first — students pick the middle number straight from the list as given (for 9, 4, 7, 2, 6 they say the median is 7, the middle position in that original order) instead of sorting least to greatest (2, 4, 6, 7, 9) and finding the true middle value, 6. Before finalizing a median, always reorder the data smallest to largest, then count to the middle position — and if there is an even number of values, average the two middle numbers.

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

Lesson 2.3Describe the Data Using the Median

Version ASupported practice

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

Learning target I can find the median of a data set and use it to describe what is typical.

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

    Put the steps for finding median in the correct order.

    Groups: Steps to find the median (in order)
    • Step 1: Order the data from least to greatest
    • Step 2: Count the total number of values
    • Step 3: Find the middle value (or average of two middle values)
    • Step 4: The middle value is the median

    Hint You must order the data FIRST before finding the middle.

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

    Find the mean of: 10, 14, 8, 12, 16

    1. A10
    2. B12
    3. C14
    4. D60

    Hint Mean means the average of all five numbers — you'll need both a total and how many numbers there are.

    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.

    Find the median of: 3, 7, 2, 9, 5

    1. A3
    2. B5
    3. C5.2
    4. D7

    Hint Median = the middle number, but only AFTER the list is in order. Don't pick the middle of the unsorted list.

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

    Find the mode of: 4, 7, 4, 9, 2, 4, 8

    1. A2
    2. B4
    3. C7
    4. D9

    Hint Mode is about repeats — which value shows up in the list more times than any other?

    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.

    Find the mean of: 6, 8, 10, 12, 14

    1. A8
    2. B10
    3. C12
    4. D50

    Hint Watch out: one tempting answer is just the total of the list. The mean asks you to go one step further.

    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.
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    The Mean Mistake (forgot to divide)

    1. 1Data setA player scored 6, 8, 10, and 6 points in 4 games.
    2. 2GoalFind the MEAN number of points.
    3. 3Add the values6 + 8 + 10 + 6 = 30
    4. 4AnswerMean = 30

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

    Hint Mean = add then DIVIDE. The total of 30 is just the sum, not the mean.

    Correct work
    Correct answer:

Explain your thinkingThe mean (43) is higher than the median (41). Why? Which better represents a typical game?

Sentence starter The mean is higher than the median because the high score of ___ pulls the mean ___. The ___ better represents a typical game because ___.

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 2.3Describe the Data Using the Median

Version BCore practice

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

Learning target I can find the median of a data set and use it to describe what is typical.

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

    Find the mean, median, and mode of each data set. Round each mean to the nearest hundredth when needed.

    Data SetMeanMedianMode
    5, 8, 8, 10, 14
    20, 25, 25, 30, 25, 35
    100, 110, 90, 100, 115, 95
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each measure to its definition.

    1. Mean
    2. Median
    3. Mode
    4. Range
    • ASum ÷ Count
    • BMiddle value
    • CMost frequent
    • DMax − Min
  3. 3Mark and label each value on the number line.

    Data: 20, 25, 30, 35, 40. Place the mean and median on the number line.

    15202530354045
    Show your thinking
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Data set: 4, 6, 6, 8, 10, 12. What is the median?

    1. A6
    2. B7
    3. C7.67
    4. D8
    Put the data in order
    Work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    The Even-Count Median Mistake

    1. 1Data setPoints per game, in order: 3, 8, 10, 14, 16, 20 (6 values)
    2. 2GoalFind the MEDIAN number of points.
    3. 3Pick the middleWith 6 values the student grabs a single middle number and says median = 10.
    4. 4AnswerMedian = 10

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

    Correct work
    Correct answer:

Explain your thinkingThe mean (43) is higher than the median (41). Why? Which better represents a typical game?

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 2.3Describe the Data Using the Median

ChallengeExtension

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

Learning target I can find the median of a data set and use it to describe what is typical.

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

    Complete the table.

    Data SetMeanMedianWhich is better & why?
    10, 12, 11, 13, 12
    10, 12, 11, 13, 50
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Stats Error

    1. 1Data set12, 15, 18, 15, 20
    2. 2Find meanSum = 80, Count = 5, Mean = 80 ÷ 5 = 16
    3. 3Find medianOrdered: 12, 15, 15, 18, 20 → Median = 15
    4. 4Find modeMode = 18 (the biggest number)

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

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A basketball player scored 15, 18, 16, 42, and 14 points in 5 games. Find the mean and median. Which better represents the player's typical game? Explain how the outlier affects each measure.

    Write your answer

Explain your thinkingThe mean (43) is higher than the median (41). Why? Which better represents a typical game?

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