To find the mean absolute deviation (MAD) for the set of points scored by the basketball team, we will follow these steps:
- Calculate the mean (average) of the data set.
- Calculate the absolute deviations from the mean for each data point.
- Calculate the mean of those absolute deviations.
Step 1: Calculate the Mean
The data set is: \[ 0, 0, 1, 1, 4, 7, 8, 9, 10, 40 \]
First, we find the sum of the points scored: \[ 0 + 0 + 1 + 1 + 4 + 7 + 8 + 9 + 10 + 40 = 80 \]
Then we calculate the mean: \[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Data Points}} = \frac{80}{10} = 8 \]
Step 2: Calculate the Absolute Deviations
Next, we calculate the absolute deviation of each data point from the mean (8):
- For 0: \( |0 - 8| = 8 \)
- For 0: \( |0 - 8| = 8 \)
- For 1: \( |1 - 8| = 7 \)
- For 1: \( |1 - 8| = 7 \)
- For 4: \( |4 - 8| = 4 \)
- For 7: \( |7 - 8| = 1 \)
- For 8: \( |8 - 8| = 0 \)
- For 9: \( |9 - 8| = 1 \)
- For 10: \( |10 - 8| = 2 \)
- For 40: \( |40 - 8| = 32 \)
Now, we list the absolute deviations: \[ 8, 8, 7, 7, 4, 1, 0, 1, 2, 32 \]
Step 3: Calculate the Mean Absolute Deviation
Now, we find the sum of the absolute deviations: \[ 8 + 8 + 7 + 7 + 4 + 1 + 0 + 1 + 2 + 32 = 70 \]
Finally, we calculate the mean absolute deviation: \[ \text{MAD} = \frac{\text{Sum of Absolute Deviations}}{\text{Number of Data Points}} = \frac{70}{10} = 7 \]
Thus, the mean absolute deviation for this set is 7.
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