Question

In statistics, Median Absolute Deviation (MAD) uses the median as the predictor and measures all the data points in the array against the median to determine how far off each data point is from that median. It then takes the absolute value (removing all negatives) for those values. Finally, it sorts the data values from smallest to largest and finds the median value from that grouping to come up with the MAD.

Where x is the array and the deviation is measured by taking the absolute value of x - median of x or |x - med of x| for each data point. To get the MAD you sort all the values and find the median of that group.
Given a x = [ -1, -1, 2 , 4 ] (average is 1 and median is .05)

Which of the below answers provides the MAD for x?

Answer 1

The Median Absolute Deviation (MAD) is calculated by first determining the absolute deviations from the median for each data point, then ordering them and finally finding the median of these deviations. For the data set x = [ -1, -1, 2 , 4 ], the MAD is 1.5.

Step-by-step explanation:

To find the Median Absolute Deviation (MAD) for the data set x = [ -1, -1, 2 , 4 ], we must first identify the median of the data, which is provided as 0.5. With this information, we calculate the absolute deviations from the median for each data point in the set:

• | -1 - 0.5 | = 1.5
• | -1 - 0.5 | = 1.5
• | 2 - 0.5 | = 1.5
• | 4 - 0.5 | = 3.5

Once we have the absolute deviations, we order them as follows: 1.5, 1.5, 1.5, 3.5. Since we have an even number of data points, the MAD is the average of the two middle values:

MAD = (1.5 + 1.5) / 2 = 1.5

Therefore, the MAD for this data set is 1.5.