For the set {6, 15, y}, the standard deviation is x. What is the stand

Official solution from Veritas Prep.

While the abstraction in this problem may make it seem like the new standard deviation cannot be calculated, in fact one core rule about standard deviation should make this one straightforward. Since standard deviation is calculated based on the difference between each term and the mean, if all terms in a set shift by the same amount (here that amount is +4), the standard deviation will remain unchanged. Here, whatever the mean is will simply increase by 4, because each term will have increased by 4. And then each term will be the same distance away from the mean as it was before - the whole scale has simply moved 4 places to the right on the number line. Therefore, because the standard deviation is the same for the new set as it was for the old, the standard deviation is again exactly x.

If you add 4 to each term in the set, the deviation won't change. For instance, take the set {6, 15, 21}

Mean = (6 + 15 + 21)/3 = 14

Distance of each term = 8, 1, 7

Now add 4 to each term, new set {10, 19, 25}, mean = 18

Distance of each term = 8, 1, 7

Voila, same standard deviation

The sets {x, y, z} and {x+k, y+k, z+k} always have the same standard deviation for any value of k.

While the abstraction in this problem may make it seem like the new standard deviation cannot be calculated, one core rule about standard deviation makes this one straightforward.


Here, whatever the mean is will simply increase by 4, because each term will have increased by 4. And then each term will be the same distance away from the mean as it was before - the whole scale has simply moved 4 places to the right on the number line.

Therefore, because the standard deviation is the same for the new set as it was for the old, the standard deviation is again exactly x.

Solution:

If each element of a data set has the same number added to it, the standard deviation of the data set doesn’t change. Since each number in the second set is 4 more than each number in the first set, the standard deviations of both sets must be the same. Therefore, the standard deviation of the second set is also x.

Answer: A

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