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Math lesson plan · 6th grade (Year 7 in England) · 45 minutes

Choose the best average and see how outliers affect it

Statistics and probability

CCSS 6.SP.B.5.DEngland: KS3 StatisticsEngland: GCSE Foundation Statistics

Objective and success criteria

Students will: Choose the best average and see how outliers affect it.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Calculate the mean, including decimal answers; Find the median of an even-sized data set

Leads to: the next skill in this area.

Materials: Squared paper for charts, Class survey data, Sticky notes for a live chart, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Calculate the mean, including decimal answers; Find the median of an even-sized data set). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Data (minutes of screen time): 49, 51, 168, 31, 62. Find the mean. → 72.2Prompt: Add all the values.
  2. Find the median: 19, 14, 10, 18, 4, 19, 8, 28 → 16Prompt: Put the values in order first.
  3. Four runners' 100 m times in seconds: 11.9, 15.8, 14, 11.5. Find the mean time. → 13.3Prompt: Add the four times carefully, lining up decimal points.

Hook · 5 min

  • Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
  • Share the objective: Choose the best average and see how outliers affect it. Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Data: 16, 14, 13, 10, 18, 88. If the outlier 88 is removed, what happens to the mean?
  • Step 1: With: 26.5; without: 14.2
  • Step 2: It decreases.
  • Answer: It decreases
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Data: 17, 10, 17, 18, 20, 0. If the outlier 0 is removed, what happens to the mean? (It increases / It decreases / It stays the same) → It increasesPrompt: Is the outlier much higher or much lower than the rest?
  2. Weekly pocket money (in dollars) in a group: 175, 31, 26, 24, 29, 31, 27. Which average best describes a typical amount? (Mean / Median) → MedianPrompt: Is there a value far from the others?

You do: independent practice · 10 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Data: 11, 30, 23, 19, 115. By how much does the mean go down when the outlier 115 is removed? Round to 1 decimal place if needed. → 18.9Prompt: Find the mean with all 5 values.
  2. Data: 20, 10, 17, 15, 12, 0. If the outlier 0 is removed, what happens to the mean? (It increases / It decreases / It stays the same) → It increasesPrompt: Is the outlier much higher or much lower than the rest?

Watch out for

  • Forgetting to put data in order before finding the median.
  • Reading a bar's height wrongly when the scale goes up in 2s or 5s.

Support and stretch

Support

  • Review first: Calculate the mean, including decimal answers.
  • Use concrete materials: squared paper for charts.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-6.

Free lesson plan from eurekami.com/lesson-plan-builder

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Choose the best average and see how outliers affect it

Name

Date

Score/ 8

  1. Question 1

    Data: 20, 14, 29, 29, 82. By how much does the mean go down when the outlier 82 is removed? Round to 1 decimal place if needed.

    Answer

  2. Question 2

    Weekly pocket money (in dollars) in a group: 20, 26, 276, 22, 20, 32, 29. Which average best describes a typical amount?

    • A. Mean
    • B. Median

  3. Question 3

    Data: 11, 20, 13, 18, 18, 2. If the outlier 2 is removed, what happens to the mean?

    • A. It increases
    • B. It decreases
    • C. It stays the same

  4. Question 4

    Data: 14, 19, 14, 28, 109. By how much does the mean go down when the outlier 109 is removed? Round to 1 decimal place if needed.

    Answer

  5. Question 5

    Weekly pocket money (in dollars) in a group: 20, 34, 32, 28, 25, 27, 201. Which average best describes a typical amount?

    • A. Mean
    • B. Median

  6. Question 6

    Data: 14, 13, 12, 20, 13, 64. If the outlier 64 is removed, what happens to the mean?

    • A. It increases
    • B. It decreases
    • C. It stays the same

  7. Question 7

    Data: 24, 17, 20, 13, 90. By how much does the mean go down when the outlier 90 is removed? Round to 1 decimal place if needed.

    Answer

  8. Question 8

    Weekly pocket money (in dollars) in a group: 28, 30, 22, 28, 35, 150, 26. Which average best describes a typical amount?

    • A. Mean
    • B. Median

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Answer key: Choose the best average and see how outliers affect it

  1. 1. 11.8

  2. 2. B. Median

  3. 3. A. It increases

  4. 4. 18.1

  5. 5. B. Median

  6. 6. B. It decreases

  7. 7. 14.3

  8. 8. B. Median