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Chapter 18: Problem 697

If \(x\) and \(y\) are related as \(2 x+5 y=15\) and mean deviation of y about mean is 10 then the mean deviation of \(x\) about mean is (a) 25 (b) 50 (c) 20 (d) 25

Short Answer

Expert verified
The mean deviation of x about its mean is 25, which is given by option (a).

Step by step solution

01

Express x in terms of y

From the given equation, we can find the relationship between x and y: \(2x + 5y = 15\) Now, we need to express x in terms of y: \(2x = 15 - 5y\) Divide both sides by 2: \(x = \frac{15 - 5y}{2}\)
02

Compute the mean deviation of x

We are given that the mean deviation of y about its mean is 10. Recall that mean deviation is the average of absolute differences between the values and their mean. Since the relationship between x and y is linear, their mean deviations are proportional to each other, and we have: Mean Deviation of x = \(\left|\frac{d(\frac{15-5y}{2})}{dy}\right|\) × Mean Deviation of y Take the derivative of x with respect to y: \( \frac{d(\frac{15-5y}{2})}{dy} = -\frac{5}{2}\) The absolute value of the derivative is: \(\left|-\frac{5}{2}\right| = \frac{5}{2}\) Now multiply by the given mean deviation of y: Mean Deviation of x = \(\frac{5}{2}\) × 10 Mean Deviation of x = 25
03

Find the answer in the given choices

The mean deviation of x about its mean is 25. Looking at the given choices, we can see that the correct answer is: (a) 25

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