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# If a, b, c, d are integers. Is standard deviation of a, b, c, d same

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Manager
Joined: 17 May 2015
Posts: 232
If a, b, c, d are integers. Is standard deviation of a, b, c, d same [#permalink]

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27 Mar 2017, 07:00
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If $$a, b, c, d$$ are integers. Is standard deviation of $$a, b, c, d$$ same as $$|a|, |b|, |c|, |d|$$ ?

(1) Mean of $$a,b,c,d$$ is 10.

(2) All numbers have the same sign.

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1186
Location: India
Re: If a, b, c, d are integers. Is standard deviation of a, b, c, d same [#permalink]

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15 Jan 2018, 23:33
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ganand wrote:
If $$a, b, c, d$$ are integers. Is standard deviation of $$a, b, c, d$$ same as $$|a|, |b|, |c|, |d|$$ ?

(1) Mean of $$a,b,c,d$$ is 10.

(2) All numbers have the same sign.

(1) Mean of a, b, c, d =10. Or their sum = 40.
Its possible that a=b=c=d=10, in which case |a|= |b|= |c|= |d| = 10. Here Std Dev of a,b,c,d = 0 and Std Dev of |a|,|b|,|c|,|d| is also 0. Both are equal.
Its also possible that a=b=30, c=d=-10. Here |a|=|b|=30, and |c|=|d|=10. Now the numbers a,b,c,d are 30, 30, -10, -10. While the numbers |a|,|b|,|c|,|d| are 30, 30, 10, 10 respectively. We can see that |a|,|b|,|c|,|d| are closer together as compared to a, b, c, d. So Std Dev of |a|,|b|,|c|,|d| will be smaller than that of a, b, c, d.

So Insufficient.

(2) All numbers are positive or all are negative. So in this case relative 'separation' among a,b,c,d will be same as that among |a|,|b|,|c|,|d|. So Std Dev will be same.
Eg, if a=2, b=3, c=4, d=5. Then |a|=2, |b|=3, |c|=4, |d|=5. Both set of numbers are exactly same. Std Dev will be equal.
If a=-2, b=-3, c=-4, d=-5, then |a|=2, |b|=3, |c|=4, |d|=5. The second set of numbers here is different from the first, but we can see that relative separation among the numbers is same. (distance between a&b is same as distance between |a| and |b|; distance between b&d is same as distance between |b| and |d|; and so on).

Sufficient.

Re: If a, b, c, d are integers. Is standard deviation of a, b, c, d same   [#permalink] 15 Jan 2018, 23:33
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