Statistics

Step 1: Arrange the data in ascending order.
The given data is 20, 5, 15, 2, 7, 3, 11.
Arranging in ascending order: 2, 3, 5, 7, 11, 15, 20.

Step 2: Calculate the mean.
Mean ( ) = .

Step 3: Calculate the mean deviation about the mean (m).
m =
m =
m = .

Step 4: Calculate the median.
Since there are 7 data points, the median is the middle value, which is 7.

Step 5: Calculate the mean deviation about the median (M).
M =
M =
M = .

Step 6: Calculate the mean of m and M.
Mean of m and M = .

Step 7: Calculate the mean deviation about the mean of m and M.
Mean of m and M = .
Mean deviation about the mean of m and M = .
Therefore, the mean deviation about the mean of m and M is .

We are given the following two conditions: Step 1: Expanding the Given Expressions Expanding the first condition: From the given condition, Expanding the second condition: From the given condition, Step 2: Adding the Two Equations Combining like terms: Step 3: Subtracting the Two Equations Simplifying: Step 4: Finding Variance The variance formula is: Substituting the known values: Step 5: Final Answer