To find the Mean Absolute Deviation (MAD), we first calculate the deviations from the mean for each data point, take the absolute values of these deviations, and then find the average of these absolute deviations.
Given data: 18, 24, 15, 9, 10
Mean (as provided) = 15.2
The formula for calculating the Mean Absolute Deviation (MAD) is: \[ \text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |x_i - \text{mean}| \] where:
- \( n \) is the number of data points,
- \( x_i \) is each individual data point,
- \( \text{mean} \) is the average of the data points.
Now let's calculate each deviation from the mean:
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For \( 18 \): \[ |18 - 15.2| = |2.8| = 2.8 \]
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For \( 24 \): \[ |24 - 15.2| = |8.8| = 8.8 \]
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For \( 15 \): \[ |15 - 15.2| = |-0.2| = 0.2 \]
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For \( 9 \): \[ |9 - 15.2| = |-6.2| = 6.2 \]
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For \( 10 \): \[ |10 - 15.2| = |-5.2| = 5.2 \]
Now, we can sum these absolute deviations: \[ 2.8 + 8.8 + 0.2 + 6.2 + 5.2 = 23.2 \]
Now, we divide by the number of data points, which is 5: \[ \text{MAD} = \frac{23.2}{5} = 4.64 \]
If we need to round that to the nearest tenth, we get: \[ \text{MAD} \approx 4.6 \]
Thus, the final equation that Leon would use to determine the Mean Absolute Deviation is: \[ \text{MAD} = \frac{1}{5} \left( |18 - 15.2| + |24 - 15.2| + |15 - 15.2| + |9 - 15.2| + |10 - 15.2| \right) \]
Calculating this gives: \[ \text{MAD} \approx \frac{1}{5} (2.8 + 8.8 + 0.2 + 6.2 + 5.2) \approx 4.6 \]
So the final form of the MAD equation is: \[ \text{MAD} = \frac{23.2}{5} \approx 4.6 \]