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 absolute deviation (MAD), we first need to find the mean of the data set provided. Based on the data provided, the mean is (88 + 85 + 90 + 75 + 99 + 100 + 77 + 76 + 92 + 82)/10 = 92. Hence, the mean without the outlier is 92.
To find the MAD, we need to calculate the absolute deviation of each data point from the mean. The absolute deviations from the mean for each data point are as follows:
|88 - 92| = 4
|85 - 92| = 7
|90 - 92| = 2
|35 - 92| = 57
|75 - 92| = 17
|99 - 92| = 7
|100 - 92| = 8
|77 - 92| = 15
|76 - 92| = 16
|92 - 92| = 0
|82 - 92| = 10
Next, we find the average of these absolute deviations. (4 + 7 + 2 + 57 + 17 + 7 + 8 + 15 + 16 + 0 + 10)/11 = 144/11 ≈ 13.09.
Therefore, the MAD of this data set is approximately 13.09.