Find the mean absolute deviation of the data set 2, 4, 6, 8.
A0
B2
C5
D6
The mean is (2 + 4 + 6 + 8)/4 = 5. The distances from 5 are 3, 1, 1 and 3. Their average is (3 + 1 + 1 + 3)/4 = 8/4 = 2. The value 5 is the mean, and 6 is the range.
Question 2 True / False
If you average the deviations from the mean without taking absolute values, you get the mean absolute deviation.
TTrue
FFalse
Answer: False
Values above the mean give positive deviations and values below give negative ones, and these always cancel exactly. The sum of signed deviations from the mean is always 0, so their average is 0 for every data set. Absolute values turn each deviation into a distance so they cannot cancel.
Question 3 Short Answer
Class A's quiz scores have mean 80 and MAD 2. Class B's scores have mean 80 and MAD 9. Describe the difference between the two classes.
Think about your answer, then reveal below.
Model answer: Both classes have the same average, but Class B's scores are much more spread out; Class A's scores are typically within about 2 points of 80, while Class B's are typically about 9 points away.
The mean describes the center and the MAD describes the typical distance from that center. Equal means with unequal MADs mean the classes are centered alike but differ in consistency.
Question 4 Short Answer
What is the MAD of the data set 7, 7, 7, 7, 7?
Think about your answer, then reveal below.
Model answer: 0
The mean is 7 and every value is exactly 7, so every distance from the mean is 0. A MAD of 0 happens only when all values are equal.