Determine the mean of the set of the data without the outlier.
88, 85, 90, 35, 75, 99, 100, 77, 76, 92, 82
Now that you know the mean without the outlier, what will the MAD be of this data?
88, 85, 90, 35, 75, 99, 100, 77, 76, 92, 82
To find the mean of the set of data without the outlier, we first need to identify the outlier. In this case, the outlier is the value 35. So, we can calculate the mean without the outlier by summing the remaining values and dividing by the number of values:
88 + 85 + 90 + 75 + 99 + 100 + 77 + 76 + 92 + 82 = 834
Now, we divide by the number of values (11) to get:
834 / 11 = 75.82
So, the mean of the set of data without the outlier is approximately 75.82.
To find the MAD (Mean Absolute Deviation) of this data, we need to subtract the mean from each value, take the absolute value, and then calculate the mean of these absolute deviations. Let's calculate this:
Absolute deviations:
|88 - 75.82| = 12.18
|85 - 75.82| = 9.18
|90 - 75.82| = 14.18
|35 - 75.82| = 40.82
|75 - 75.82| = 0.82
|99 - 75.82| = 23.18
|100 - 75.82| = 24.18
|77 - 75.82| = 1.18
|76 - 75.82| = 0.18
|92 - 75.82| = 16.18
|82 - 75.82| = 6.18
Mean of absolute deviations:
(12.18 + 9.18 + 14.18 + 40.82 + 0.82 + 23.18 + 24.18 + 1.18 + 0.18 + 16.18 + 6.18) / 11 = 10.09
So, the MAD of this data is approximately 10.09.