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Difference Means Mads 7B3B75

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1. **State the problem:** We are given the means and mean absolute deviations (MADs) of runners' race times for two years and asked to explain the difference of the means in terms of the MADs. 2. **Given data:** - Year 1 mean = 16.2 seconds, MAD = 1.5 - Year 2 mean = 20.5 seconds, MAD = 1.5 3. **Calculate the difference of the means:** $$\text{Difference} = 20.5 - 16.2 = 4.3$$ 4. **Express the difference in terms of MADs:** Since each MAD is 1.5, divide the difference by MAD: $$\frac{4.3}{1.5} = \frac{\cancel{4.3}}{\cancel{1.5}} \approx 2.87$$ 5. **Interpretation:** The difference between the means is about 2.87 MADs, which is closest to 3 MADs. 6. **Conclusion:** This suggests there is likely a small amount of overlap between the two data sets because the means differ by about 3 MADs. **Final answer:** The difference between the means is about 3 MADs. There is likely a small amount of overlap between the data sets.