Math Problem Statement
Week
1
2
3
4
5
6
Value
19
12
15
10
18
14 calculate the mean absolute error for this data
Solution
To calculate the Mean Absolute Error (MAE), we need to compute the average of the absolute differences between each observed value and the mean of the dataset.
Step 1: Calculate the mean of the values
Step 2: Compute the absolute errors
&|19 - 14.67| = 4.33 \\ &|12 - 14.67| = 2.67 \\ &|15 - 14.67| = 0.33 \\ &|10 - 14.67| = 4.67 \\ &|18 - 14.67| = 3.33 \\ &|14 - 14.67| = 0.67 \\ \end{aligned}$$ ### Step 3: Calculate the mean of these absolute errors $$\text{MAE} = \frac{\text{Sum of Absolute Errors}}{\text{Number of Values}}$$ $$\text{MAE} = \frac{4.33 + 2.67 + 0.33 + 4.67 + 3.33 + 0.67}{6}$$ $$\text{MAE} = \frac{16}{6} = 2.67$$ ### Final Answer: The **Mean Absolute Error (MAE)** for this data is **2.67**. Let me know if you want a detailed explanation or visual representation of the steps! --- ### Relative Questions: 1. How do you interpret the MAE value in this context? 2. What would happen to the MAE if an extreme outlier were added to the dataset? 3. How does MAE differ from Mean Squared Error (MSE)? 4. Can you provide an example where MAE might not be a suitable metric? 5. How is MAE useful in real-world applications like forecasting? ### Tip: Always double-check the calculation of absolute differences to ensure accuracy when computing MAE.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean Absolute Error
Averages
Formulas
Mean = (Sum of Values) / (Number of Values)
Absolute Error = |Value - Mean|
MAE = (Sum of Absolute Errors) / (Number of Values)
Theorems
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Suitable Grade Level
Grades 8-10
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