Final answer:
To find the mean deviation about the median for the given data set, first find the median and then calculate the absolute deviation from each data value to the median. Sum up the absolute deviations and divide by the number of values.
Step-by-step explanation:
To find the mean deviation about the median, we first need to find the median of the given data set. The data set is: 2, 9, 7, 25, 6, 9, 9, 4, 6, 5, 8, 39. To find the median, we arrange the data in ascending order: 2, 4, 5, 6, 6, 7, 8, 9, 9, 9, 25, 39. Since there are 12 data values, the median is the average of the 6th and 7th values, which is (7 + 8) / 2 = 7.5.
To find the mean deviation about the median, we calculate the absolute deviation from each data value to the median, sum them up, and divide by the number of values. The absolute deviations from the median are: 5.5, 0.5, 1.5, 0.5, 1.5, 0.5, 0.5, 1.5, 1.5, 0.5, 17.5, 31.5. Summing them up, we get 62.5. Finally, dividing by 12 (the number of values), we get the mean deviation about the median: 62.5 / 12 = 5.21.