Mean Absolute Deviation activity - Free Printable

To solve this problem, we need to find the Mean Absolute Deviation (MAD) for each of the four data sets.

Here is the step-by-step process for each set:
1. Find the Mean: Add up all the numbers and divide by how many numbers there are.
2. Find the Differences: Subtract the mean from each data point.
3. Find the Absolute Values: Make sure all differences are positive (remove the negative sign).
4. Find the Mean of the Absolute Values: Add up all the absolute differences and divide by the count of numbers. This is the MAD.

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Problem 1: 26, 25, 30, 40, 50, 65

Step 1: Find the Mean
* Sum: $26 + 25 + 30 + 40 + 50 + 65 = 236$
* Count: 6
* Mean: $236 \div 6 \approx 39.33$

*Note: This result is a repeating decimal. In many school worksheets, if the numbers don't divide evenly, it suggests a potential typo in the problem or they expect rounding. Let's re-check the sum. $26+25=51$, $51+30=81$, $81+40=121$, $121+50=171$, $171+65=236$. The math is correct. Let's proceed with rounding to two decimal places for calculation, or perhaps the problem intended a cleaner mean. Let's assume standard rounding to 2 decimals: 39.33.*

Step 2 & 3: Differences and Absolute Values
* $|26 - 39.33| = |-13.33| = 13.33$
* $|25 - 39.33| = |-14.33| = 14.33$
* $|30 - 39.33| = |-9.33| = 9.33$
* $|40 - 39.33| = |0.67| = 0.67$
* $|50 - 39.33| = |10.67| = 10.67$
* $|65 - 39.33| = |25.67| = 25.67$

Step 4: Mean Absolute Deviation
* Sum of Absolute Differences: $13.33 + 14.33 + 9.33 + 0.67 + 10.67 + 25.67 = 74$
* MAD: $74 \div 6 \approx 12.33$

*(Self-Correction/Refinement: Often in these worksheets, the Mean is an integer. If the sum 236 is correct, the mean is not an integer. Let's look at the other problems. If Problem 1 is meant to be clean, maybe I misread a number? No, the image is clear. I will provide the answer based on the calculated mean of 39.33.)*

Result 1:
Mean: 39.33
Sum of Absolute Differences: 74
Mean Absolute Deviation: 12.33

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Problem 2: 80, 75, 35, 56, 78, 90, 40

Step 1: Find the Mean
* Sum: $80 + 75 + 35 + 56 + 78 + 90 + 40 = 454$
* Count: 7
* Mean: $454 \div 7 \approx 64.86$

Step 2 & 3: Differences and Absolute Values
* $|80 - 64.86| = 15.14$
* $|75 - 64.86| = 10.14$
* $|35 - 64.86| = 29.86$
* $|56 - 64.86| = 8.86$
* $|78 - 64.86| = 13.14$
* $|90 - 64.86| = 25.14$
* $|40 - 64.86| = 24.86$

Step 4: Mean Absolute Deviation
* Sum of Absolute Differences: $15.14 + 10.14 + 29.86 + 8.86 + 13.14 + 25.14 + 24.86 = 127.14$
* MAD: $127.14 \div 7 \approx 18.16$

*(Observation: These numbers are messy. Let's re-read the numbers. 80, 75, 35, 56, 78, 90, 40. Sum is 454. 454/7 is definitely not an integer. I will proceed with the calculated values.)*

Result 2:
Mean: 64.86
Sum of Absolute Differences: 127.14
Mean Absolute Deviation: 18.16

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Problem 3: 24, 45, 50, 30, 65, 80

Step 1: Find the Mean
* Sum: $24 + 45 + 50 + 30 + 65 + 80 = 294$
* Count: 6
* Mean: $294 \div 6 = 49$ (This is a clean integer!)

Step 2 & 3: Differences and Absolute Values
* $|24 - 49| = |-25| = 25$
* $|45 - 49| = |-4| = 4$
* $|50 - 49| = |1| = 1$
* $|30 - 49| = |-19| = 19$
* $|65 - 49| = |16| = 16$
* $|80 - 49| = |31| = 31$

Step 4: Mean Absolute Deviation
* Sum of Absolute Differences: $25 + 4 + 1 + 19 + 16 + 31 = 96$
* MAD: $96 \div 6 = 16$

Result 3:
Mean: 49
Sum of Absolute Differences: 96
Mean Absolute Deviation: 16

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Problem 4: 10, 9, 7, 15, 6, 7, 3

Step 1: Find the Mean
* Sum: $10 + 9 + 7 + 15 + 6 + 7 + 3 = 57$
* Count: 7
* Mean: $57 \div 7 \approx 8.14$

Step 2 & 3: Differences and Absolute Values
* $|10 - 8.14| = 1.86$
* $|9 - 8.14| = 0.86$
* $|7 - 8.14| = 1.14$
* $|15 - 8.14| = 6.86$
* $|6 - 8.14| = 2.14$
* $|7 - 8.14| = 1.14$
* $|3 - 8.14| = 5.14$

Step 4: Mean Absolute Deviation
* Sum of Absolute Differences: $1.86 + 0.86 + 1.14 + 6.86 + 2.14 + 1.14 + 5.14 = 19.14$
* MAD: $19.14 \div 7 \approx 2.73$

Result 4:
Mean: 8.14
Sum of Absolute Differences: 19.14
Mean Absolute Deviation: 2.73

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Summary of Tables to Fill:

Problem 1:
* Mean: 39.33
* Differences: -13.33, -14.33, -9.33, 0.67, 10.67, 25.67
* Absolute: 13.33, 14.33, 9.33, 0.67, 10.67, 25.67
* Sum (Absolute): 74
* MAD: 12.33

Problem 2:
* Mean: 64.86
* Differences: 15.14, 10.14, -29.86, -8.86, 13.14, 25.14, -24.86
* Absolute: 15.14, 10.14, 29.86, 8.86, 13.14, 25.14, 24.86
* Sum (Absolute): 127.14
* MAD: 18.16

Problem 3:
* Mean: 49
* Differences: -25, -4, 1, -19, 16, 31
* Absolute: 25, 4, 1, 19, 16, 31
* Sum (Absolute): 96
* MAD: 16

Problem 4:
* Mean: 8.14
* Differences: 1.86, 0.86, -1.14, 6.86, -2.14, -1.14, -5.14
* Absolute: 1.86, 0.86, 1.14, 6.86, 2.14, 1.14, 5.14
* Sum (Absolute): 19.14
* MAD: 2.73

Final Answer:
Problem 1:
Mean: 39.33
Sum of Absolute Differences: 74
Mean Absolute Deviation: 12.33

Problem 2:
Mean: 64.86
Sum of Absolute Differences: 127.14
Mean Absolute Deviation: 18.16

Problem 3:
Mean: 49
Sum of Absolute Differences: 96
Mean Absolute Deviation: 16

Problem 4:
Mean: 8.14
Sum of Absolute Differences: 19.14
Mean Absolute Deviation: 2.73