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anonymous
 one year ago
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 yvalues corresponding to all the xvalues the greatest?
anonymous
 one year ago
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 yvalues corresponding to all the xvalues the greatest?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436830799377:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i need to know how....

Jacob902
 one year ago
Best ResponseYou've already chosen the best response.0It 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
 one year ago
Best ResponseYou've already chosen the best response.0Assuming \(X\) 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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