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

Lesson 2.32.3 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the median of a data set and use it to describe what is typical — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can find the median of a data set and use it to describe what is typical — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    012345678910Test scores
    The same scores, in order.

    Find the median of these test scores: 6, 2, 9, 4, 7.

    1. 1Put the scores in order from least to greatest.
    2. 2How many scores are there?
    3. 3Cross off one score from each end until one is left. What is it?
    Final answer:
  2. 2Complete each step, then write the final answer.
    54555657585960616263middlemiddle
    Two middle values this time.

    Find the median of these heights in inches: 58, 62, 55, 60.

    1. 1Put the heights in order. How many are there?
    2. 2There is an even count. Name the two middle values.
    3. 3Find the number halfway between them: (58 + 60) ÷ 2.
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the median of this data set: 3, 8, 5, 1, 9.

    Show your work

    Hint Put the values in order first. Then find the one in the middle.

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

    Find the median of this data set: 12, 4, 10, 6.

    Show your work

    Hint There are 4 values. Find the two middle values after you order them.

    Final answer:
  5. 5Complete each step, then write the final answer.
    024681012141618202224Years teaching

    Five teachers have taught for 3, 15, 7, 22 and 10 years. What is the median number of years?

    Show your work

    Hint Order the years from least to greatest. The middle one is the median.

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

    Mia says the median of 9, 2, 7 is 2 because 2 is in the middle of the list. Is she right? What is the median?

    Show your work

    Hint Mia skipped a step. What must you do to the values first?

    Final answer:

Explain your thinkingWhy must you put the values in order before you find the median? Use Mia's mistake to explain.

Sentence starter First I put the values in order because ___. · The median is ___ because it is ___.

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