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Bunuel
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If each data point in a certain set Q is increased by a factor of 7 11 May 2021, 04:45
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C
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55% (hard)

Question Stats:

42% (00:43) correct 58% (00:40) wrong based on 175 sessions

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If each data point in a certain set Q, with nonzero standard deviation, is increased by a factor of 7, what happens with the set's standard deviation?

A. Doesn't Change
B. Decreases by Factor 7
C. Increases by Factor 7
D. Increases by 7
E. Can't be determined
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C
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If each data point in a certain set Q is increased by a factor of 7 11 May 2021, 05:43
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Bunuel
If each data point in a certain set Q, with nonzero standard deviation, is increased by a factor of 7, what happens with the set's standard deviation?

A. Doesn't Change
B. Decreases by Factor 7
C. Increases by Factor 7
D. Increases by 7
E. Can't be determined
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We know that adding a constant to all the data points, doesn't affect the SD.
Multiplying a constant to all the data points, increases the SD by that factor.

If I understood the question correctly, it is talking about adding a factor of 7 to all the data points!
IMO A.
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If each data point in a certain set Q is increased by a factor of 7 12 May 2021, 13:34
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Bunuel
If each data point in a certain set Q, with nonzero standard deviation, is increased by a factor of 7, what happens with the set's standard deviation?

A. Doesn't Change
B. Decreases by Factor 7
C. Increases by Factor 7
D. Increases by 7
E. Can't be determined
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The question says that the each data point is increased by factor of 7 --> This means each data point is multiplied with 7

We know the concept that whenever the data points are multiplied by certain constant then the standard deviation is also multiplied by that factor.

Hence the answer will be C
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If each data point in a certain set Q is increased by a factor of 7 11 Jun 2021, 08:05
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Hi Bunuel,
Why option C is the answer?
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If each data point in a certain set Q is increased by a factor of 7 11 Jun 2021, 08:30
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bv8562
Hi Bunuel,
Why option C is the answer?
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If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

So, if we increase each data point by 7, then the SD will also increase 7 times.
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If each data point in a certain set Q is increased by a factor of 7 12 Jun 2021, 06:03
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Hi Bunuel,
Why option C is the answer?

If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

So, if we increase each data point by 7, then the SD will also increase 7 times.
Show more

Hey Bunuel,
Could you please explain this with an example? Because what I understand from the language given in question "each data point in a certain set Q is increased by a factor of 7" is that each data point is increased by a number which is supposed to be a factor of 7. So, essentially we are just adding a constant to each data point. So, based on this factor the SD of new set should not change.
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If each data point in a certain set Q is increased by a factor of 7 12 Jun 2021, 06:37
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bv8562
Bunuel
bv8562
Hi Bunuel,
Why option C is the answer?

If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

So, if we increase each data point by 7, then the SD will also increase 7 times.

Hey Bunuel,
Could you please explain this with an example? Because what I understand from the language given in question "each data point in a certain set Q is increased by a factor of 7" is that each data point is increased by a number which is supposed to be a factor of 7. So, essentially we are just adding a constant to each data point. So, based on this factor the SD of new set should not change.
Show more

Increased by a factor of x means multiplied by x.
Decreased by a factor of x means divided by x.

So, increased by a factor of 7 means multiplied by 7.
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If each data point in a certain set Q is increased by a factor of 7 12 Sep 2022, 00:26
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