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If two variables x and y are related by 2x 3y - 7 = 0 and the mean and mean deviation about mean of x are 1 and 0.3 respectively , then the coefficient of mean deviation of y about its mean is?
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If two variables x and y are related by 2x 3y - 7 = 0 and the mean a...
Given:
- Two variables x and y are related by the equation 2x - 3y - 7 = 0.
- The mean of x is 1.
- The mean deviation about the mean of x is 0.3.

To find:
- The coefficient of mean deviation of y about its mean.

Explanation:

Step 1: Find the mean deviation of x about its mean:
The mean deviation about the mean is given by the formula:

Mean Deviation = (Σ|xi - x̄|) / N

Where:
- Σ denotes the sum of,
- |xi - x̄| denotes the absolute difference between each value xi and the mean x̄,
- N denotes the total number of values.

Given that the mean of x is 1 and the mean deviation about the mean of x is 0.3, we can write:

0.3 = (Σ|xi - 1|) / N

Step 2: Find the mean deviation of y about its mean:
Now, let's find the mean deviation of y about its mean. To do this, we need to express y in terms of x from the given equation:

2x - 3y - 7 = 0

Rearranging this equation, we get:

2x - 7 = 3y

Dividing both sides by 3, we get:

(2/3)x - 7/3 = y

Now we have y in terms of x. Let's substitute this expression for y in the mean deviation formula:

Mean Deviation of y = (Σ|yi - ȳ|) / N

Where:
- Σ denotes the sum of,
- |yi - ȳ| denotes the absolute difference between each value yi and the mean ȳ,
- N denotes the total number of values.

Since y is expressed in terms of x, we can rewrite this as:

Mean Deviation of y = (Σ|((2/3)xi - 7/3) - ȳ|) / N

Step 3: Calculate the coefficient of mean deviation of y about its mean:
The coefficient of mean deviation is given by the formula:

Coefficient of Mean Deviation = Mean Deviation / Mean

In this case, the mean of x is 1. So, we can substitute the value of the mean deviation of y and the mean of x into the formula to find the coefficient of mean deviation of y about its mean.

Conclusion:
By following the above steps, we can find the coefficient of mean deviation of y about its mean.
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If two variables x and y are related by 2x 3y - 7 = 0 and the mean and mean deviation about mean of x are 1 and 0.3 respectively , then the coefficient of mean deviation of y about its mean is?
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