Mean Deviation about Mode of the given numbers

The given numbers are: 4/11, 6/11, 8/11, 9/11, 12/11, 8/11

Step 1: Finding the mode

The mode is the number that appears most frequently in the given set of numbers. In this case, 8/11 appears twice, which is more than any other number. Hence, the mode is 8/11.

Step 2: Finding the deviation of each number from the mode

To find the deviation of each number from the mode, we subtract the mode from each number.

Deviation of 4/11 from 8/11 = 8/11 - 4/11 = 4/11
Deviation of 6/11 from 8/11 = 8/11 - 6/11 = 2/11
Deviation of 8/11 from 8/11 = 8/11 - 8/11 = 0
Deviation of 9/11 from 8/11 = 9/11 - 8/11 = 1/11
Deviation of 12/11 from 8/11 = 12/11 - 8/11 = 4/11
Deviation of 8/11 from 8/11 = 8/11 - 8/11 = 0

Step 3: Finding the absolute deviation of each number from the mode

To find the absolute deviation of each number from the mode, we take the absolute value of the deviation.

Absolute deviation of 4/11 from 8/11 = |4/11| = 4/11
Absolute deviation of 6/11 from 8/11 = |2/11| = 2/11
Absolute deviation of 8/11 from 8/11 = |0| = 0
Absolute deviation of 9/11 from 8/11 = |1/11| = 1/11
Absolute deviation of 12/11 from 8/11 = |4/11| = 4/11
Absolute deviation of 8/11 from 8/11 = |0| = 0

Step 4: Finding the mean deviation about mode

Mean deviation about mode = (Sum of absolute deviation of each number from the mode) / (Total number of numbers)

Mean deviation about mode = [(4/11) + (2/11) + 0 + (1/11) + (4/11) + 0] / 6

Mean deviation about mode = (11/11) / 6

Mean deviation about mode = 11/66

Therefore, the mean deviation about mode for the given numbers is 11/66.