Here are the solutions to the problems on your worksheet, broken down step-by-step.
EXAMPLE Section
Problem: Find the MAD of this data set: 10, 8, 5, 7, 9, 11, 13.
Step 1: Find the mean (average).
Add all the numbers together and divide by how many numbers there are (7).
$$10 + 8 + 5 + 7 + 9 + 11 + 13 = 63$$
$$63 \div 7 = 9$$
The mean is
9.
Step 2 & 3: Find the absolute difference from the mean.
Subtract the mean (9) from each number. If the answer is negative, make it positive (absolute value).
* $|10 - 9| = 1$
* $|8 - 9| = 1$
* $|5 - 9| = 4$
* $|7 - 9| = 2$
* $|9 - 9| = 0$
* $|11 - 9| = 2$
* $|13 - 9| = 4$
The differences are:
1, 1, 4, 2, 0, 2, 4
Step 4: Find the average of the differences.
Add the differences together and divide by 7.
$$1 + 1 + 4 + 2 + 0 + 2 + 4 = 14$$
$$14 \div 7 = 2$$
Answer for Example: The MAD is
2.
***
"You try" Section
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Problem 1
Task: Find the mean absolute deviation of the data set: 17, 16, 13, 3, 27, 11, 5
Step 1: Find the mean.
There are 7 numbers.
Sum: $17 + 16 + 13 + 3 + 27 + 11 + 5 = 92$
Mean: $92 \div 7 \approx 13.14$
Step 2 & 3: Find the absolute differences.
* $|17 - 13.14| = 3.86$
* $|16 - 13.14| = 2.86$
* $|13 - 13.14| = 0.14$
* $|3 - 13.14| = 10.14$
* $|27 - 13.14| = 13.86$
* $|11 - 13.14| = 2.14$
* $|5 - 13.14| = 8.14$
Step 4: Find the average of the differences.
Sum of differences: $3.86 + 2.86 + 0.14 + 10.14 + 13.86 + 2.14 + 8.14 = 41.14$
MAD: $41.14 \div 7 \approx 5.88$
Answer for #1: The MAD is approximately
5.88.
***
####
Problem 2
Task: Mrs. Stanford recorded her class's test scores: 71, 80, 95, 52, 86, 88, 100, 75, 79, 81. How spread out were the students' test scores? Use MAD to find out.
Step 1: Find the mean.
There are 10 scores.
Sum: $71 + 80 + 95 + 52 + 86 + 88 + 100 + 75 + 79 + 81 = 807$
Mean: $807 \div 10 = 80.7$
Step 2 & 3: Find the absolute differences.
* $|71 - 80.7| = 9.7$
* $|80 - 80.7| = 0.7$
* $|95 - 80.7| = 14.3$
* $|52 - 80.7| = 28.7$
* $|86 - 80.7| = 5.3$
* $|88 - 80.7| = 7.3$
* $|100 - 80.7| = 19.3$
* $|75 - 80.7| = 5.7$
* $|79 - 80.7| = 1.7$
* $|81 - 80.7| = 0.3$
Step 4: Find the average of the differences.
Sum of differences: $9.7 + 0.7 + 14.3 + 28.7 + 5.3 + 7.3 + 19.3 + 5.7 + 1.7 + 0.3 = 93$
MAD: $93 \div 10 = 9.3$
Answer for #2: The MAD is
9.3. This means, on average, the test scores are about 9.3 points away from the class average.
Final Answer:
Example: 2
You Try #1: ~5.88
You Try #2: 9.3
Parent Tip: Review the logic above to help your child master the concept of mean absolute deviation worksheet answers.
