Given:

Relation between x and y: 5y-3x=10

Mean deviation about mean for x: 12


To find:

Mean deviation of y about mean


Solution:

We need to find the mean deviation of y about mean, which is given by the formula:

Mean deviation of y about mean = (1/n) * Σ|yi - ȳ|

where yi is the ith value of y, ȳ is the mean of y and n is the total number of values of y.


To find ȳ, we can rearrange the given equation in terms of y:

5y - 3x = 10

5y = 3x + 10

y = (3/5)x + 2


So, the mean of y is:

ȳ = (1/n) * Σyi

We can express yi in terms of x using the given equation:

5y - 3x = 10

y = (3/5)x + 2

So, yi = (3/5)xi + 2


Substituting this in the formula for ȳ, we get:

ȳ = (1/n) * Σ[(3/5)xi + 2]

ȳ = (3/5) * (1/n) * Σxi + (2/n) * Σ1

ȳ = (3/5) * x̄ + 2

where x̄ is the mean of x.


Now, we can use the formula for mean deviation of y about mean:

Mean deviation of y about mean = (1/n) * Σ|yi - ȳ|

Substituting the expression for yi, ȳ and x̄, we get:

Mean deviation of y about mean = (1/n) * Σ|[(3/5)xi + 2] - [(3/5)x̄ + 2]|

Mean deviation of y about mean = (3/5) * (1/n) * Σ|xi - x̄|

Mean deviation of y about mean = (3/5) * Mean deviation about mean for x

Mean deviation of y about mean = (3/5) * 12

Mean deviation of y about mean = 7.2


Therefore, the mean deviation of y about mean is 7.2.