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Range and mean absolute deviation worksheet

Grade 6 math, Common Core 6.SP.B.5c. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Range and mean absolute deviation

Grade 6 math, Common Core 6.SP.B.5c

Find the range and the mean absolute deviation (MAD). Round to the nearest tenth if needed.

  1. 1.
    Data: 16, 19, 9, 16
  2. 2.
    Data: 21, 14, 17, 17, 11
  3. 3.
    Data: 37, 40, 43, 42, 39, 39
  4. 4.
    Data: 18, 21, 21, 24
  5. 5.
    Data: 22, 22, 18, 27, 21
  6. 6.
    Data: 27, 25, 29, 29, 30
  7. 7.
    Data: 11, 13, 15, 16, 10, 13
  8. 8.
    Data: 26, 26, 24, 32
  9. 9.
    Data: 34, 32, 29, 29
  10. 10.
    Data: 34, 34, 44, 48, 45
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Range and mean absolute deviation

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. Range 10, MAD 3

    Mean: 60 ÷ 4 = 15Distances: 1, 4, 6, 1MAD: 12 ÷ 4 = 3

  2. 2. Range 10, MAD 2.8

    Mean: 80 ÷ 5 = 16Distances: 5, 2, 1, 1, 5MAD: 14 ÷ 5 = 2.8

  3. 3. Range 6, MAD 1.7

    Mean: 240 ÷ 6 = 40Distances: 3, 0, 3, 2, 1, 1MAD: 10 ÷ 6 = 1.67

  4. 4. Range 6, MAD 1.5

    Mean: 84 ÷ 4 = 21Distances: 3, 0, 0, 3MAD: 6 ÷ 4 = 1.5

  5. 5. Range 9, MAD 2

    Mean: 110 ÷ 5 = 22Distances: 0, 0, 4, 5, 1MAD: 10 ÷ 5 = 2

  6. 6. Range 5, MAD 1.6

    Mean: 140 ÷ 5 = 28Distances: 1, 3, 1, 1, 2MAD: 8 ÷ 5 = 1.6

  7. 7. Range 6, MAD 1.7

    Mean: 78 ÷ 6 = 13Distances: 2, 0, 2, 3, 3, 0MAD: 10 ÷ 6 = 1.67

  8. 8. Range 8, MAD 2.5

    Mean: 108 ÷ 4 = 27Distances: 1, 1, 3, 5MAD: 10 ÷ 4 = 2.5

  9. 9. Range 5, MAD 2

    Mean: 124 ÷ 4 = 31Distances: 3, 1, 2, 2MAD: 8 ÷ 4 = 2

  10. 10. Range 14, MAD 5.6

    Mean: 205 ÷ 5 = 41Distances: 7, 7, 3, 7, 4MAD: 28 ÷ 5 = 5.6

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About range and mean absolute deviation

The range is the biggest value minus the smallest. The mean absolute deviation (MAD) tells you how far the values are from the mean, on average: find the mean, find how far each value is from it, then find the mean of those distances. A small MAD means the data is close together.

Worked example 1

Data: 28, 29, 30, 28, 35
  1. Step 1.Mean: 150 ÷ 5 = 30
  2. Step 2.Distances: 2, 1, 0, 2, 5
  3. Step 3.MAD: 10 ÷ 5 = 2

Answer: Range 7, MAD 2

Worked example 2

Data: 28, 18, 22, 22, 23, 25
  1. Step 1.Mean: 138 ÷ 6 = 23
  2. Step 2.Distances: 5, 5, 1, 1, 0, 2
  3. Step 3.MAD: 14 ÷ 6 = 2.33

Answer: Range 10, MAD 2.3

Worked example 3

Data: 30, 29, 18, 20, 18
  1. Step 1.Mean: 115 ÷ 5 = 23
  2. Step 2.Distances: 7, 6, 5, 3, 5
  3. Step 3.MAD: 26 ÷ 5 = 5.2

Answer: Range 12, MAD 5.2

Watch out for

  • Distances from the mean are never negative.
  • Divide by the number of values, not by the range.
  • A data set with a bigger MAD is more spread out.

Practice range and mean absolute deviation online

On StudyWiz, your kid can practice range and mean absolute deviation with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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