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Each of the following linear equations defines y as a function of x

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Joined: 07 Jan 2019
Posts: 63
Concentration: International Business, Finance
WE: Engineering (Manufacturing)
Each of the following linear equations defines y as a function of x  [#permalink]

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New post 22 May 2019, 08:49
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

41% (01:44) correct 59% (01:57) wrong based on 17 sessions

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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 is the standard deviation of the y-values corresponding to all the x-values the greatest?


A) y = x/3
B) y = x/2+40
C) y = x
D) y = 2x + 50
E) y = 3x − 20
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Re: Each of the following linear equations defines y as a function of x  [#permalink]

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New post 22 May 2019, 09:27
1
When we add a constant number to every value in a set, we don't change how spread out that set is. So we don't change the sets standard deviation. So if you create a set of one hundred values by plugging x = 1, 2, 3, ... 98, 99, 100 into the equation

y = 3x + 10,000

you'll get the same standard deviation that you get when you plug those x-values into

y = 3x

because the sets only differ because we're adding the constant 10,000 to every value in the first set.

So we can ignore the numbers we're adding on at the end in each answer choice; we're just comparing these:

y = (1/3)x
y = (1/2)x
y = x
y = 2x
y = 3x

If you multiply all the values in a set by some constant, you stretch distances out (or shrink them, if we multiply by something between 0 and 1). So if we plug in 1, 2, 3, ... 100 into y = 3x, the distances between values will be 3 times as big as they are when we plug those numbers into y = x. So we'll get a larger standard deviation (in fact, one that is precisely 3 times larger). So E is the right answer here.
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Re: Each of the following linear equations defines y as a function of x   [#permalink] 22 May 2019, 09:27
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