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Umnica [9.8K]
3 years ago
9

Consider a population list x, with a CV= 10%. A second population list, y, has a CV= 20%. Assume that the average of list y is 1

0 times the average of list x. What is the variance of list y if the variance of list x is 100?
Business
1 answer:
Sedaia [141]3 years ago
3 0

Answer:

s^2_Y = 200^2= 40000

Explanation:

Data given

From the info given we have the following conditions:

\bar Y = 10 \bar X

s^2_x = 100

s_x = 10

CV_x = 10\% = 0.1

CV_y = 20\% = 0.2

And we want to find s^2_y =?

Solution to the problem

From the definition of variation coefficient we know this:

CV_x = 0.1=\frac{S_x}{\bar X}

From this condition we can solve for \bar X and we got:

\bar X = \frac{10}{0.1}=100

Now we can find \bar Y like this:

\bar Y = 10*100 = 1000

Now from the definition for coefficient of variation for Y we have:

CV_y = 0.2=\frac{S_y}{\bar Y}

We can solve for S_y and we got:

S_y = 0.2*1000= 200

And finally the variance would be:

s^2_Y = 200^2= 40000

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