Find the absolute mean deviation for the set {X, 2x, 3x, 4x}

Given:

Data set =

To find:

The absolute mean deviation for the given set.

Solution:

We have,

Data set =

Mean of the data set is

Now,

The formula for mean absolute deviation (MAD) is

Therefore, the mean absolute deviation for the given set of data is x.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: