Mean Absolute Deviation Quiz: Finding Mean Absolute Deviation

1) What does Mean Absolute Deviation (MAD) measure?

How spread out data values are from the mean

The total of all data points

The highest value in the data set

The average of the data values

MAD measures how much the data values deviate, on average, from the mean.

Explanation

MAD measures how much the data values deviate, on average, from the mean.

2) Which of the following steps comes first in finding MAD?

Find the mean of the data set

Square each data value

Find the mode

Divide by total number of data points

Step 1: Find the mean of the data set.

Explanation

Step 1: Find the mean of the data set.

3) What is the second step in finding MAD?

Add all deviations

Find absolute deviations from the mean

Find range

Find median

After finding the mean, calculate how far each data point is from the mean, ignoring negative signs.

Explanation

After finding the mean, calculate how far each data point is from the mean, ignoring negative signs.

4) The Mean Absolute Deviation is the __________ of the absolute deviations.

mean (average); MAD uses absolute deviations so that negative differences do not cancel positives.

Explanation

mean (average); MAD uses absolute deviations so that negative differences do not cancel positives.

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5) Find the mean of {2, 4, 6, 8}.

4

5

6

8

Mean = (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4 = 5.

Explanation

Mean = (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4 = 5.

6) For data {2, 4, 6, 8}, mean = 5. What are the deviations?

{-3, -1, 1, 3}

{-2, 0, 2, 4}

{-4, -2, 0, 2}

{-1, 0, 1, 2}

Each value − mean: 2−5=−3, 4−5=−1, 6−5=1, 8−5=3.

Explanation

Each value − mean: 2−5=−3, 4−5=−1, 6−5=1, 8−5=3.

7) What are the absolute deviations for {2, 4, 6, 8} with mean 5?

{3, 1, 1, 3}

{−3, −1, 1, 3}

{4, 2, 0, 2}

{2, 1, 3, 4}

Take absolute values of deviations: |−3|=3, |−1|=1, |1|=1, |3|=3.

Explanation

Take absolute values of deviations: |−3|=3, |−1|=1, |1|=1, |3|=3.

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9) What is the Mean Absolute Deviation (MAD) for {2, 4, 6, 8}?

1

2

3

4

MAD = 8 ÷ 4 = 2.

Explanation

MAD = 8 ÷ 4 = 2.

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10) Absolute deviations can be negative.

True

False

Absolute deviations are always positive because they show distance from the mean.

Explanation

Absolute deviations are always positive because they show distance from the mean.

11) Find the mean of {3, 5, 7}.

4

5

6

7

Mean = (3 + 5 + 7) ÷ 3 = 15 ÷ 3 = 5.

Explanation

Mean = (3 + 5 + 7) ÷ 3 = 15 ÷ 3 = 5.

12) Find the absolute deviations for {3, 5, 7} with mean 5.

{1, 0, 1}

{2, 0, 2}

{3, 0, 3}

{4, 0, 4}

Mean = (3 + 5 + 7) ÷ 3 = 5

Deviations: 3 − 5 = −2, 5 − 5 = 0, 7 − 5 = 2

Absolute deviations = {2, 0, 2}

Explanation

Mean = (3 + 5 + 7) ÷ 3 = 5

Deviations: 3 − 5 = −2, 5 − 5 = 0, 7 − 5 = 2

Absolute deviations = {2, 0, 2}

13) Sum of absolute deviations for {3, 5, 7} is:

2

4

6

8

2 + 0 + 2 = 4.

Explanation

2 + 0 + 2 = 4.

14) What is MAD for {3, 5, 7}?

1

1.33

3

2

Step 1: Mean = (3 + 5 + 7) ÷ 3 = 5

Step 2: Absolute deviations = |3−5|, |5−5|, |7−5| = {2, 0, 2}

Step 3: Sum = 2 + 0 + 2 = 4

Step 4: MAD = 4 ÷ 3 = 1.33

Explanation

Step 1: Mean = (3 + 5 + 7) ÷ 3 = 5

Step 2: Absolute deviations = |3−5|, |5−5|, |7−5| = {2, 0, 2}

Step 3: Sum = 2 + 0 + 2 = 4

Step 4: MAD = 4 ÷ 3 = 1.33

15) MAD formula is: MAD = (Sum of __________ deviations) ÷ number of data points.

MAD = (Sum of absolute deviations) ÷ number of data points.

Explanation

MAD = (Sum of absolute deviations) ÷ number of data points.

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16) Select all correct steps to find MAD.

Find the mean

Find each deviation

Take absolute deviations

Add them

Divide by the number of data points

Steps: Mean → deviations → absolute deviations → add them → divide by n.

Explanation

Steps: Mean → deviations → absolute deviations → add them → divide by n.

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17) For {10, 12, 14, 16}, what is the mean?

11

12

13

14

Mean = (10+12+14+16) ÷ 4 = 52 ÷ 4 = 13.

Explanation

Mean = (10+12+14+16) ÷ 4 = 52 ÷ 4 = 13.

18) For data {10, 12, 14, 16}, mean = 13. What are the absolute deviations?

{3, 1, 1, 3}

{−3, −1, 1, 3}

{2, 0, 2, 4}

{4, 2, 0, 2}

|10−13|=3, |12−13|=1, |14−13|=1, |16−13|=3.

Explanation

|10−13|=3, |12−13|=1, |14−13|=1, |16−13|=3.

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19) Sum of absolute deviations for {10, 12, 14, 16} is:

6

8

10

12

3+1+1+3 = 8.

Explanation

3+1+1+3 = 8.

20) MAD for {10, 12, 14, 16} is:

1

2

3

4

MAD = 8 ÷ 4 = 2.

Explanation

MAD = 8 ÷ 4 = 2.