To find the correct expression that represents the ratio of the difference of the two means to Sidney’s mean absolute deviation, we first need to calculate the difference between the means of Sidney and Phil.
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Calculate the difference of the means: \[ \text{Difference} = \text{Sidney's Mean} - \text{Phil's Mean} = 82 - 78 = 4 \]
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Sidney's Mean Absolute Deviation: Sidney's mean absolute deviation is given as \(3.28\).
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Set up the ratio: We need the ratio of the difference of the means to Sidney's mean absolute deviation: \[ \text{Ratio} = \frac{\text{Difference of Means}}{\text{Sidney's Mean Absolute Deviation}} = \frac{4}{3.28} \]
Now, let's check the provided options to see which one matches:
- \( \frac{82}{3.28} \) — This is incorrect as it is using Sidney's mean instead of the difference.
- \( \frac{4}{3.28} \) — This is correct as it represents the ratio we calculated.
- \( \frac{4}{0.68} \) — This is incorrect as it does not match our calculation.
- \( \frac{82}{0.68} \) — This is incorrect as it also does not match our calculation.
Thus, the correct expression that represents the ratio of the difference of the two means to Sidney’s mean absolute deviation is: \[ \frac{4}{3.28} \]