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

Lesson 2.32.3 Small Group · Group 2

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, explain how I can tell, and judge a case I have not seen before.

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)
Mean, Median, and ModeSpanish: Media, mediana y moda Measures that describe a data set's center: average, middle value, and most frequent value. For 2, 3, 3, 8: mean = 4, median = 3, mode = 3.

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 2.32.3 Small Group · Group 2

Group 2Challenge 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, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    048121620242832Data values

    Find the median of 15, 4, 9, 30, 6, 11. Is it a good typical value?

    1. 1Order the values. Which two are in the middle?
    2. 2What is the median?
    3. 3How many values are less than the median? How many are greater?
    Final answer:
  2. 2Complete each step, then write the final answer.

    Six numbers have a median of 10. Five of them are 3, 6, 12, 15 and 20. The missing number is between 6 and 12. Find it.

    1. 1Put the missing number in the order. Which two values are in the middle?
    2. 2The two middle values average to 10. What must they add to?
    3. 3What is the missing number?
    4. 4Why does only the middle pair matter, not 3 or 20?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the median of 2.5, 4, 1.5, 6, 3.

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

    Four scores have a median of 15. Three scores are 10, 14 and 20. The missing score is between 14 and 20. Find it.

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

    House prices on a street are $210,000, $195,000, $230,000, $205,000 and $890,000. What is the median price?

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

    Jon says adding the value 50 to 3, 5, 6, 8 will raise the median by a lot. What is the new median?

    Show your work
    Final answer:

Explain your thinkingA coach says one player's 40 points makes the team look great. Should the coach report the median or the mean? Defend your choice.

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