Testinar Grade 8 math

Mean Absolute Deviation

Learn to reason about and solve Grade 8 problems involving Mean Absolute Deviation.

CH06-05 Statistics, Data, and Probability
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Find the Mean Absolute Deviation (MAD) of the data set \(\{2, 4, 6, 8, 10\}\).

    1. \(2\)
    2. \(2.4\)
    3. \(3\)
    4. \(6\)

  2. The mean of the data set \(\{3, 5, 7, 9\}\) is \(6\). What is the Mean Absolute Deviation?

    1. \(1\)
    2. \(2\)
    3. \(3\)
    4. \(4\)

  3. Which data set has a MAD of \(2\)?

    1. \(\{1, 2, 3, 4, 5\}\)
    2. \(\{2, 4, 6, 10\}\)
    3. \(\{5, 7, 9, 11\}\)
    4. \(\{1, 3, 5, 9\}\)

  4. The data set \(\{10, 12, 14, 16\}\) has a mean of \(13\). What is the MAD?

    1. \(1\)
    2. \(1.5\)
    3. \(2\)
    4. \(3\)

  5. For the data \(\{4, 4, 8, 8\}\), the mean is \(6\). Calculate the MAD.

    1. \(0\)
    2. \(2\)
    3. \(4\)
    4. \(6\)

  6. The data set is \(\{1, 2, 3, 4, 5, 6\}\). What is the MAD? (Mean \(= 3.5\))

    1. \(1.5\)
    2. \(2\)
    3. \(1.75\)
    4. \(2.5\)

  7. Data: \(\{5, 5, 5, 5, 5\}\). What is the MAD?

    1. \(0\)
    2. \(1\)
    3. \(5\)
    4. \(25\)

  8. Which interpretation of MAD is correct?

    1. MAD tells you the largest value in the data
    2. MAD measures the typical distance of data points from the mean
    3. MAD is always equal to the mean
    4. MAD is usually negative
Teacher and parent reference

Answer key and explanations

  1. B. \(2.4\)

    Mean \(=6\). Absolute deviations: \(|2-6|=4,\ |4-6|=2,\ |6-6|=0,\ |8-6|=2,\ |10-6|=4\). Sum \(=12\). MAD \(=12/5=2.4\).

  2. B. \(2\)

    Absolute deviations: \(|3-6|=3,\ |5-6|=1,\ |7-6|=1,\ |9-6|=3\). Sum \(=8\). MAD \(=8/4=2\).

  3. C. \(\{5, 7, 9, 11\}\)

    Mean \(=8\). Absolute deviations: \(|5-8|=3,\ |7-8|=1,\ |9-8|=1,\ |11-8|=3\). Sum \(=8\). MAD \(=8/4=2\).

  4. C. \(2\)

    Absolute deviations: \(|10-13|=3,\ |12-13|=1,\ |14-13|=1,\ |16-13|=3\). Sum \(=8\). MAD \(=8/4=2\).

  5. B. \(2\)

    Absolute deviations: \(|4-6|=2,\ |4-6|=2,\ |8-6|=2,\ |8-6|=2\). Sum \(=8\). MAD \(=8/4=2\).

  6. A. \(1.5\)

    Absolute deviations: \(|1-3.5|=2.5,\ |2-3.5|=1.5,\ |3-3.5|=0.5,\ |4-3.5|=0.5,\ |5-3.5|=1.5,\ |6-3.5|=2.5\). Sum \(=9\). MAD \(=9/6=1.5\).

  7. A. \(0\)

    Mean \(=5\). All values equal the mean, so all deviations are \(0\). MAD \(=0/5=0\).

  8. B. MAD measures the typical distance of data points from the mean

    MAD represents the average distance each value is from the mean, showing variability. It cannot be negative because it uses absolute values.

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