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22 May 2019, 08:49
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E
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Difficulty:
55%
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Question Stats:
62% (01:36) correct
38%
(01:34)
wrong
based on 289
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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
A) y = x/3
B) y = x/2+40
C) y = x
D) y = 2x + 50
E) y = 3x − 20
22 May 2019, 09:27
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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.
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.
General Discussion
13 Dec 2024, 07:29
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SD is nothing but the spread of numbers from the mean. Simply plug x=100 and x=1 in each of the equations to get the relative spread. Constant values don't change anything, so keep em or remove em, doesn't matter. Greatest spread is the answer, so.
X=1,100
a. y= 1/3 and 100/3 ->.33 and 33.33 --> spread of 33
b. y= 1/2+40 and 100/2+40 -> 40.5 and 90 --> spread of 49.5
c. y= 1 and 100 --> spread of 99
d. y= 2*1 + 50 and 2*100 + 50 -> 52 and 200 --> spread of 148
e. y= 3*1 - 20 and 3*100 - 20 -> -17 and 280 --> spread of 297
hence answer is E.
X=1,100
a. y= 1/3 and 100/3 ->.33 and 33.33 --> spread of 33
b. y= 1/2+40 and 100/2+40 -> 40.5 and 90 --> spread of 49.5
c. y= 1 and 100 --> spread of 99
d. y= 2*1 + 50 and 2*100 + 50 -> 52 and 200 --> spread of 148
e. y= 3*1 - 20 and 3*100 - 20 -> -17 and 280 --> spread of 297
hence answer is E.
