Key HWK Mean Absolute Deviation | PDF - Free Printable
Educational worksheet: Key HWK Mean Absolute Deviation | PDF. Download and print for classroom or home learning activities.
JPG
768×1024
159.1 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #651492
⭐
Show Answer Key & Explanations
Step-by-step solution for: Key HWK Mean Absolute Deviation | PDF
▼
Show Answer Key & Explanations
Step-by-step solution for: Key HWK Mean Absolute Deviation | PDF
Let’s solve each problem step by step. We’re finding the Mean Absolute Deviation (MAD) for each set of numbers.
---
Step 1: Find the Mean
Add all numbers:
10 + 7 + 13 + 10 + 8 = 48
Divide by count (5):
48 ÷ 5 = 9.6
✔ Mean = 9.6
---
Step 2: Find Difference from Mean (Data - Mean)
- 10 - 9.6 = +0.4
- 7 - 9.6 = -2.6
- 13 - 9.6 = +3.4
- 10 - 9.6 = +0.4
- 8 - 9.6 = -1.6
---
Step 3: Take Positive Values (Absolute Values)
- |+0.4| = 0.4
- |-2.6| = 2.6
- |+3.4| = 3.4
- |+0.4| = 0.4
- |-1.6| = 1.6
---
Step 4: Add the Positive Values
0.4 + 2.6 + 3.4 + 0.4 + 1.6 = 8.4
---
Step 5: Divide by Count to Get MAD
8.4 ÷ 5 = 1.68
✔ Final Answer for Problem 1: 1.68
---
Step 1: Find the Mean
Add all numbers:
110 + 114 + 104 + 108 + 106 = 542
Divide by count (5):
542 ÷ 5 = 108.4
✔ Mean = 108.4
---
Step 2: Find Difference from Mean
- 110 - 108.4 = +1.6
- 114 - 108.4 = +5.6
- 104 - 108.4 = -4.4
- 108 - 108.4 = -0.4
- 106 - 108.4 = -2.4
---
Step 3: Take Positive Values
- |+1.6| = 1.6
- |+5.6| = 5.6
- |-4.4| = 4.4
- |-0.4| = 0.4
- |-2.4| = 2.4
---
Step 4: Add the Positive Values
1.6 + 5.6 + 4.4 + 0.4 + 2.4 = 14.4
---
Step 5: Divide by Count to Get MAD
14.4 ÷ 5 = 2.88
✔ Final Answer for Problem 2: 2.88
---
Step 1: Find the Mean
Add all numbers:
87 + 75 + 85 + 77 + 74 + 82 + 90 + 88 + 79 + 81 = 818
Divide by count (10):
818 ÷ 10 = 81.8
✔ Mean = 81.8
---
Step 2: Find Difference from Mean
- 87 - 81.8 = +5.2
- 75 - 81.8 = -6.8
- 85 - 81.8 = +3.2
- 77 - 81.8 = -4.8
- 74 - 81.8 = -7.8
- 82 - 81.8 = +0.2
- 90 - 81.8 = +8.2
- 88 - 81.8 = +6.2
- 79 - 81.8 = -2.8
- 81 - 81.8 = -0.8
---
Step 3: Take Positive Values
- 5.2, 6.8, 3.2, 4.8, 7.8, 0.2, 8.2, 6.2, 2.8, 0.8
---
Step 4: Add the Positive Values
5.2 + 6.8 = 12
12 + 3.2 = 15.2
15.2 + 4.8 = 20
20 + 7.8 = 27.8
27.8 + 0.2 = 28
28 + 8.2 = 36.2
36.2 + 6.2 = 42.4
42.4 + 2.8 = 45.2
45.2 + 0.8 = 46.0
✔ Sum = 46.0
---
Step 5: Divide by Count to Get MAD
46.0 ÷ 10 = 4.6
✔ Final Answer for Problem 3: 4.6
---
Step 1: Find the Mean
Add all numbers:
15 + 17 + 15 + 17 + 21 + 17 + 15 + 23 + 20 + 18 = 178
Divide by count (10):
178 ÷ 10 = 17.8
✔ Mean = 17.8
---
Step 2: Find Difference from Mean
- 15 - 17.8 = -2.8
- 17 - 17.8 = -0.8
- 15 - 17.8 = -2.8
- 17 - 17.8 = -0.8
- 21 - 17.8 = +3.2
- 17 - 17.8 = -0.8
- 15 - 17.8 = -2.8
- 23 - 17.8 = +5.2
- 20 - 17.8 = +2.2
- 18 - 17.8 = +0.2
---
Step 3: Take Positive Values
- 2.8, 0.8, 2.8, 0.8, 3.2, 0.8, 2.8, 5.2, 2.2, 0.2
---
Step 4: Add the Positive Values
2.8 + 0.8 = 3.6
3.6 + 2.8 = 6.4
6.4 + 0.8 = 7.2
7.2 + 3.2 = 10.4
10.4 + 0.8 = 11.2
11.2 + 2.8 = 14.0
14.0 + 5.2 = 19.2
19.2 + 2.2 = 21.4
21.4 + 0.2 = 21.6
✔ Sum = 21.6
---
Step 5: Divide by Count to Get MAD
21.6 ÷ 10 = 2.16
✔ Final Answer for Problem 4: 2.16
---
Final Answer:
Problem 1: 1.68
Problem 2: 2.88
Problem 3: 4.6
Problem 4: 2.16
---
🔢 Problem 1: Data Set → 10, 7, 13, 10, 8
Step 1: Find the Mean
Add all numbers:
10 + 7 + 13 + 10 + 8 = 48
Divide by count (5):
48 ÷ 5 = 9.6
✔ Mean = 9.6
---
Step 2: Find Difference from Mean (Data - Mean)
- 10 - 9.6 = +0.4
- 7 - 9.6 = -2.6
- 13 - 9.6 = +3.4
- 10 - 9.6 = +0.4
- 8 - 9.6 = -1.6
---
Step 3: Take Positive Values (Absolute Values)
- |+0.4| = 0.4
- |-2.6| = 2.6
- |+3.4| = 3.4
- |+0.4| = 0.4
- |-1.6| = 1.6
---
Step 4: Add the Positive Values
0.4 + 2.6 + 3.4 + 0.4 + 1.6 = 8.4
---
Step 5: Divide by Count to Get MAD
8.4 ÷ 5 = 1.68
✔ Final Answer for Problem 1: 1.68
---
🔢 Problem 2: Data Set → 110, 114, 104, 108, 106
Step 1: Find the Mean
Add all numbers:
110 + 114 + 104 + 108 + 106 = 542
Divide by count (5):
542 ÷ 5 = 108.4
✔ Mean = 108.4
---
Step 2: Find Difference from Mean
- 110 - 108.4 = +1.6
- 114 - 108.4 = +5.6
- 104 - 108.4 = -4.4
- 108 - 108.4 = -0.4
- 106 - 108.4 = -2.4
---
Step 3: Take Positive Values
- |+1.6| = 1.6
- |+5.6| = 5.6
- |-4.4| = 4.4
- |-0.4| = 0.4
- |-2.4| = 2.4
---
Step 4: Add the Positive Values
1.6 + 5.6 + 4.4 + 0.4 + 2.4 = 14.4
---
Step 5: Divide by Count to Get MAD
14.4 ÷ 5 = 2.88
✔ Final Answer for Problem 2: 2.88
---
🔢 Problem 3: Data Set → 87, 75, 85, 77, 74, 82, 90, 88, 79, 81
Step 1: Find the Mean
Add all numbers:
87 + 75 + 85 + 77 + 74 + 82 + 90 + 88 + 79 + 81 = 818
Divide by count (10):
818 ÷ 10 = 81.8
✔ Mean = 81.8
---
Step 2: Find Difference from Mean
- 87 - 81.8 = +5.2
- 75 - 81.8 = -6.8
- 85 - 81.8 = +3.2
- 77 - 81.8 = -4.8
- 74 - 81.8 = -7.8
- 82 - 81.8 = +0.2
- 90 - 81.8 = +8.2
- 88 - 81.8 = +6.2
- 79 - 81.8 = -2.8
- 81 - 81.8 = -0.8
---
Step 3: Take Positive Values
- 5.2, 6.8, 3.2, 4.8, 7.8, 0.2, 8.2, 6.2, 2.8, 0.8
---
Step 4: Add the Positive Values
5.2 + 6.8 = 12
12 + 3.2 = 15.2
15.2 + 4.8 = 20
20 + 7.8 = 27.8
27.8 + 0.2 = 28
28 + 8.2 = 36.2
36.2 + 6.2 = 42.4
42.4 + 2.8 = 45.2
45.2 + 0.8 = 46.0
✔ Sum = 46.0
---
Step 5: Divide by Count to Get MAD
46.0 ÷ 10 = 4.6
✔ Final Answer for Problem 3: 4.6
---
🔢 Problem 4: Data Set → 15, 17, 15, 17, 21, 17, 15, 23, 20, 18
Step 1: Find the Mean
Add all numbers:
15 + 17 + 15 + 17 + 21 + 17 + 15 + 23 + 20 + 18 = 178
Divide by count (10):
178 ÷ 10 = 17.8
✔ Mean = 17.8
---
Step 2: Find Difference from Mean
- 15 - 17.8 = -2.8
- 17 - 17.8 = -0.8
- 15 - 17.8 = -2.8
- 17 - 17.8 = -0.8
- 21 - 17.8 = +3.2
- 17 - 17.8 = -0.8
- 15 - 17.8 = -2.8
- 23 - 17.8 = +5.2
- 20 - 17.8 = +2.2
- 18 - 17.8 = +0.2
---
Step 3: Take Positive Values
- 2.8, 0.8, 2.8, 0.8, 3.2, 0.8, 2.8, 5.2, 2.2, 0.2
---
Step 4: Add the Positive Values
2.8 + 0.8 = 3.6
3.6 + 2.8 = 6.4
6.4 + 0.8 = 7.2
7.2 + 3.2 = 10.4
10.4 + 0.8 = 11.2
11.2 + 2.8 = 14.0
14.0 + 5.2 = 19.2
19.2 + 2.2 = 21.4
21.4 + 0.2 = 21.6
✔ Sum = 21.6
---
Step 5: Divide by Count to Get MAD
21.6 ÷ 10 = 2.16
✔ Final Answer for Problem 4: 2.16
---
Final Answer:
Problem 1: 1.68
Problem 2: 2.88
Problem 3: 4.6
Problem 4: 2.16
Parent Tip: Review the logic above to help your child master the concept of mean absolute deviation worksheet answers.
