Understanding Mean Absolute Deviation Quiz

  • 6th Grade
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| By Thames
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| Questions: 20 | Updated: Dec 11, 2025
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1) Data set A (daily quiz scores out of 10): 7, 9, 8, 8, 8, 7, 9, 8 What is the mean of Data set A?

Explanation

 To find the mean, you add all the values, then divide by how many there are.

The total of the scores is 64, and there are 8 data points.

64 ÷ 8 = 8.0.

So the mean is 8.0.

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About This Quiz
Understanding Mean Absolute Deviation Quiz - Quiz

This quiz will help you explore Mean Absolute Deviation (MAD), a cool statistic that shows how consistent or spread out data points are from the average. You’ll get hands-on with data sets, calculate deviations, and use MAD to analyze whether data is tightly packed or wildly inconsistent. By the end,... see moreyou'll understand how to measure the "typical distance" from the mean and why this matters in real-world data!
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2) What does deviation from the mean represent for a single score?

Explanation

 A deviation tells you how far a score is from the mean.

It’s simply the score minus the mean, showing whether the score is above or below the average.

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3) Why do we use absolute value when calculating MAD?

Explanation

Deviations can be negative or positive, but we don’t want them to cancel each other out.

Using absolute value makes all deviations positive so we can measure the total spread accurately.

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4) Which list shows the absolute deviations from the mean for Data set A?

Explanation

 The mean is 8.

Subtract 8 from each score and take the absolute value.

That gives: 1, 1, 0, 0, 0, 1, 1, 0.

So option A is correct.

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5) What is the MAD of Data set A?

Explanation

 First, add up the absolute deviations: they total 4.

Then divide by the 8 data points: 4 ÷ 8 = 0.5.

So the MAD is 0.5, meaning the scores are usually half a point away from the mean.

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6) What does the MAD in question 5 tell you about consistency?

Explanation

 A MAD of 0.5 is small, meaning the scores don’t vary much.

Most scores are close to the mean, so they are fairly consistent.

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7) Which data set has a MAD of 0? (Data set B: 3, 7, 11, 5, 9; Data set C: 7, 7, 7, 7, 7)

Explanation

 A MAD of 0 means all values are exactly the same as the mean.

Data set C is 7, 7, 7, 7, 7 — no variation at all.

Data set B has different numbers, so its MAD is not zero.

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8) Which statement best compares the spreads of Data sets B and C?

Explanation

 Data set C has no spread because every number is 7.

Data set B has numbers above and below 7, so it has more variation.

Therefore, B has more spread than C.

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9) If the mean of Data set B is 7, what is the absolute deviation of the value 11?

Explanation





 Deviation is the distance from the mean:

11 − 7 = 4, and |4| = 4.

But check the choices: the intended mean is 8?

Actually, Data set B is 3, 7, 11, 5, 9 and its mean is 7.

The absolute deviation is |11 − 7| = 4.

The correct choice is C (4).

(Note: You listed answer choices A–D as 2, 3, 4, 5. The correct absolute deviation is 4 → option C.)
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10) Which interpretation of MAD is most accurate?

Explanation

 MAD measures the typical distance of values from the mean.

It tells you, on average, how far the data points are from the center.

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11) Who is more consistent based on MAD? (Runner D: 8, 9, 8, 10, 7, 8; Runner E: 8, 8, 8, 8, 8, 8)

Explanation

 Runner E has the same time every day, so the deviations are all zero.

That gives a MAD of 0, meaning perfect consistency.

Runner D’s times vary, so Runner E is more consistent.

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12) If both runners have the same mean, what does a larger MAD imply?

Explanation

 A larger MAD means the data points vary more from day to day.

So a larger MAD means less consistency and more changes in performance.

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13) Which change would decrease Runner D's MAD the most?

Explanation

Runner D’s most unusual value is 10, which is far above the mean.

Replacing it with 8 brings it much closer to the average, reducing its deviation.

This change reduces the spread more than the other options.

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14) If Runner D's MAD is approximately 1, what does that mean?

Explanation

 A MAD of 1 means each day’s time is usually about 1 minute away from the average time.

It describes the typical amount of variation in the runner’s performance.

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15) Which class likely has the larger MAD? (Class F: 6,7,7,8,8,9; Class G: 2,5,8,10,10,10)

Explanation

Class F’s scores range from 6 to 9—close together.

Class G ranges from 2 to 10—much more spread out.

More spread means a bigger MAD.

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16) Which measure would best show that Class G has more inconsistent scores?

Explanation

A higher MAD means more variation and less consistency.

Since Class G has more spread, it would have a higher MAD.

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17) If both classes have the same mean, which statement could still be true?

Explanation

 Having the same mean doesn’t force them to have the same variability.

Class F could be more consistent, meaning it could have a smaller MAD even if the averages match.

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18) Which data set has the greatest MAD?

Explanation

 Data set B goes from 3 to 11, spread evenly across that range.

Large variation leads to a larger typical distance from the mean.

The other sets have smaller spreads or repeated values, so B has the greatest MAD.

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19) What happens to the MAD if each data value increases by 5?

Explanation

MAD depends on how far values are from the mean — not the actual size of the numbers.

Adding 5 to every value (and to the mean) keeps all distances the same.

So the MAD stays the same.

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20) Which single statement best captures what MAD represents?

Explanation

 MAD is the typical distance from the mean, and we use absolute value to avoid negatives.

It’s a measure of consistency or spread in the data.

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Data set A (daily quiz scores out of 10): 7, 9, 8, 8, 8, 7, 9, 8 ...
What does deviation from the mean represent for a single score?
Why do we use absolute value when calculating MAD?
Which list shows the absolute deviations from the mean for Data set A?
What is the MAD of Data set A?
What does the MAD in question 5 tell you about consistency?
Which data set has a MAD of 0? (Data set B: 3, 7, 11, 5, 9; Data set...
Which statement best compares the spreads of Data sets B and C?
If the mean of Data set B is 7, what is the absolute deviation of the...
Which interpretation of MAD is most accurate?
Who is more consistent based on MAD? (Runner D: 8, 9, 8, 10, 7, 8;...
If both runners have the same mean, what does a larger MAD imply?
Which change would decrease Runner D's MAD the most?
If Runner D's MAD is approximately 1, what does that mean?
Which class likely has the larger MAD? (Class F: 6,7,7,8,8,9; Class G:...
Which measure would best show that Class G has more inconsistent...
If both classes have the same mean, which statement could still be...
Which data set has the greatest MAD?
What happens to the MAD if each data value increases by 5?
Which single statement best captures what MAD represents?
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