Interpreting Mean Absolute Deviation In Real-World Contexts Quiz

1) A scientist measures the growth of plants using two different fertilizers. Fertilizer X results in a MAD of 1.2 cm, while Fertilizer Y results in a MAD of 3.8 cm. What does this indicate?

Fertilizer X produces more consistent growth

Fertilizer Y produces more consistent growth

Both fertilizers are equally effective

Fertilizer Y produces taller plants

Lower MAD means more consistent growth. Fertilizer X is more reliable.

Explanation

Lower MAD means more consistent growth. Fertilizer X is more reliable.

2) A delivery service tracks package delivery times. If the MAD is 30 minutes, what does this tell customers?

All packages arrive at exactly the same time

The mean delivery time is 30 minutes

Delivery times vary by about 30 minutes on average from the mean

The service is unreliable

MAD shows how much times differ from the average. On average, 30 minutes difference.

Explanation

MAD shows how much times differ from the average. On average, 30 minutes difference.

3) Two students practice free throws. Student A has a MAD of 2 baskets made per session, and Student B has a MAD of 6 baskets made per session. Which student's performance is more predictable?

Student A

Student B

Both are equally predictable

The student with the higher mean

Smaller MAD = more predictable performance. Student A is more consistent.

Explanation

Smaller MAD = more predictable performance. Student A is more consistent.

4) A quality control inspector finds that Product Line 1 has a MAD of 0.02 inches in measurements, while Product Line 2 has a MAD of 0.15 inches. If consistency is the most important factor, which product line should be recommended?

Product Line 2

Product Line 1

Both are equally acceptable

The one with the larger mean measurement

Lower MAD means more consistent measurements. Product Line 1 is better.

Explanation

Lower MAD means more consistent measurements. Product Line 1 is better.

5) What is the mean (average) number of points scored by Player A?

13

14

15

16

Add all scores (12+15+14+13+16+14+15+13=112). Divide by 8 → 112 ÷ 8 = 14.

Explanation

Add all scores (12+15+14+13+16+14+15+13=112). Divide by 8 → 112 ÷ 8 = 14.

6) What is the MAD (Mean Absolute Deviation) for Player A's scores?

0.5

1

1.5

2

The average distance of scores from the mean (14) is about 1.5.

Explanation

The average distance of scores from the mean (14) is about 1.5.

7) The MAD for Player B's scores is 4.5. Which player is more consistent in their scoring?

Player A, because their MAD is lower

Player B, because their MAD is higher

Player A, because their mean is higher

Both players are equally consistent

Smaller MAD means more consistent performance. Player A’s MAD is lower.

Explanation

Smaller MAD means more consistent performance. Player A’s MAD is lower.

8) What does the MAD tell us about Player B's performance?

Player B always scores more points than Player A

Player B is more reliable than Player A

Player B's mean score is lower than Player A's

Player B's scores vary more from game to game

A higher MAD means scores vary more from game to game.

Explanation

A higher MAD means scores vary more from game to game.

9) What is the mean number of books read in Class 1?

5

5.5

6

6.5

Add all numbers (5+5+5+6+6+7+7+7=48). Divide by 8 → 48 ÷ 8 = 6.

Explanation

Add all numbers (5+5+5+6+6+7+7+7=48). Divide by 8 → 48 ÷ 8 = 6.

10) The MAD for Class 1 is 0.75. What does this indicate about the students' reading habits?

Students read very different amounts

The mean is not accurate

Students read similar amounts

Students did not enjoy reading

A small MAD means most students read about the same number of books.

Explanation

A small MAD means most students read about the same number of books.

11) The MAD for Class 2 is 2.5. How does the variability in Class 2 compare to Class 1?

Class 2 has less variability

Class 2 has more variability

Both classes have the same variability

Class 2's mean is higher

A higher MAD shows greater variation in the number of books read.

Explanation

A higher MAD shows greater variation in the number of books read.

12) If a teacher wants students to read a consistent number of books each month, which class is closer to meeting that goal?

Class 1, because the MAD is lower

Class 2, because the MAD is higher

Both classes are equally consistent

Neither class is consistent

Lower MAD means Class 1’s students are more consistent readers.

Explanation

Lower MAD means Class 1’s students are more consistent readers.

13) A factory produces light bulbs. Factory X has a MAD of 50 hours for bulb lifespan, while Factory Y has a MAD of 15 hours. What does this tell you?

Factory Y produces bulbs with more consistent lifespans

Factory X produces bulbs that last longer

Factory X is more reliable

The mean lifespan is the same for both factories

A smaller MAD means more consistent results. Factory Y is more consistent.

Explanation

A smaller MAD means more consistent results. Factory Y is more consistent.

14) Two weather stations recorded daily temperatures. Station A has a MAD of 3°F and Station B has a MAD of 8°F. Which statement is true?

Station B has more stable temperatures

Both stations have equally variable temperatures

Station A has more stable temperatures

Station B's mean temperature is higher

A lower MAD means temperatures at Station A change less.

Explanation

A lower MAD means temperatures at Station A change less.

15) What is the mean sprint time for Runner 1?

11.2

11.3

11.4

11.5

Add all times (11.2+11.5+11.3+11.4+11.6+11.4=68.4). Divide by 6 → 68.4 ÷ 6 = 11.4.

Explanation

Add all times (11.2+11.5+11.3+11.4+11.6+11.4=68.4). Divide by 6 → 68.4 ÷ 6 = 11.4.

16) The MAD for Runner 1 is approximately 0.10 seconds. What does this suggest?

Runner 1's times vary greatly

Runner 1's times are very consistent

Runner 1 is slower than Runner 2

The mean is not useful

A very small MAD means Runner 1’s times are almost the same each run.

Explanation

A very small MAD means Runner 1’s times are almost the same each run.

17) The MAD for Runner 2 is approximately 0.65 seconds. If the coach wants to select the most reliable runner for a competition, who should they choose?

Runner 1, because they have a lower MAD

Runner 2, because they have a higher MAD

Both runners are equally reliable

Runner 2, because they have a lower mean

Lower MAD = more reliable performance. Runner 1 is more consistent.

Explanation

Lower MAD = more reliable performance. Runner 1 is more consistent.

18) A company tracks customer wait times at two locations. Location A has a MAD of 2 minutes and Location B has a MAD of 7 minutes. Which location provides a more predictable customer experience?

Location B

Location A

Both are equally predictable

Cannot be determined without the mean

Lower MAD means wait times are more predictable at Location A.

Explanation

Lower MAD means wait times are more predictable at Location A.