anonymous
  • anonymous
Each of the following linear equations defines y as a function of x for all integers x from 1 to 100. For which of the following equations id the standard deviation of the y-values corresponding to all the x-values the greatest?
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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Jacob902
  • Jacob902
e
anonymous
  • anonymous
i need to know how....

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Jacob902
  • Jacob902
It is obviously unpractical to actually calculate the SD for x values 1 to 100. SD is the measure of how spread out values in a set are. In a linear equation, you are going to have a upper and lower limit with all other values falling in between linearly and evenly. So basically in ambiguous GRE question speak, you are being asked : which of the equations have a higher spread of x values? If you substitute the biggest and smallest value of x in all the equations, you'll see that option E has x values lying between -17 and 280. So it must have the greatest SD. Hope this makes sense.
ybarrap
  • ybarrap
Assuming \(X\) is a random integer between 1 and 100. Standard deviation is the square root of variance. In each of your equations, if \(X\) is the random variable, then a constant \(a\) times \(X\) multiplies the variance by \(a^2\) $$ Var(aX)=a^2\operatorname{Var}(X). $$ This means that the standard deviation is multiplied by \(a\), because standard deviation is the square root of variance. The variance of a constant is zero, so you can ignore them. Which \(x\) has the largest constant multiplying it? That is the one with the highest standard deviation. https://en.wikipedia.org/wiki/Variance#Basic_properties

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