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The problem asks which data set shows greater variability, using the given Mean Absolute Deviation (MAD) values for two data sets.

- **Data set A**:
  - Mean = 43.5
  - MAD = 3.7

- **Data set B**:
  - Mean = 12.8
  - MAD = 4.1

### Explanation:
MAD (Mean Absolute Deviation) measures the average distance between each data point and the mean of the data set, which reflects the variability in the data.

In this case:
- The MAD for **Data Set A** is 3.7, while the MAD for **Data Set B** is 4.1. Even though **Data Set A** has a larger mean (43.5 vs. 12.8), **Data Set B** has a higher MAD.
- Since **Data Set B** has a higher MAD, it shows greater variability because its data points are, on average, further from the mean than those of Data Set A.

### Conclusion:
**Data Set B** shows greater variability based on the MAD values.

Would you like further details or have any questions?

### Related Questions:
1. How does MAD compare to other measures of variability, such as standard deviation?
2. How do outliers affect the MAD in a data set?
3. Can two data sets have the same MAD but different variances?
4. Why might one prefer using MAD over variance for analyzing data variability?
5. How does the scale of the data (such as a large mean) affect the interpretation of MAD?

**Tip**: When comparing variability, always focus on how MAD or standard deviation values differ rather than just comparing the means of the data sets.

Which data set shows greater variability? Explain your reasoning.

This problem compares two data sets using their Mean Absolute Deviation (MAD) values. Data set A has a mean of 43.5 and MAD of 3.7, while data set B has a mean of 12.8 and MAD of 4.1. Learn how MAD measures data variability and why Data Set B shows greater variability despite having a smaller mean.

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