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Standard deviation

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Ramit88 Rising GMAT Star
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Standard deviation Post Thu Jan 20, 2011 3:22 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If sets A & B have the same number of terms, is the Standard deviation of set A greater than the Standard deviation of set B ?

    1. the range of set A is greater than the range of B
    2. sets A & B are both evenly spaced sets

    ANS:C

    but i read somewhere if sets have same no. of digits then the set with higher range have greater Standard deviation .. can someone please explain this to me

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    Post Thu Jan 20, 2011 7:34 am
    IMO A

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    Post Thu Jan 20, 2011 8:13 am
    ramit,

    Consider this example:
    A={-3,0,0,0,0,0,3}
    Number of terms =7
    range = 6
    mean =0
    sd = sqrt(18/7)

    B={-2,-2,-2,0,2,2,2}
    Number of terms =7
    range = 4
    mean =0
    sd = sqrt(24/7)

    N(A) = N(B)
    Range(A)>Range(B)
    SD(A) < SD(B)

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    Post Fri Jan 21, 2011 12:43 am
    jaxis wrote:
    ramit,

    Consider this example:
    A={-3,0,0,0,0,0,3}
    Number of terms =7
    range = 6
    mean =0
    sd = sqrt(18/7)

    B={-2,-2,-2,0,2,2,2}
    Number of terms =7
    range = 4
    mean =0
    sd = sqrt(24/7)

    N(A) = N(B)
    Range(A)>Range(B)
    SD(A) < SD(B)
    BUT

    if you take B = {-2,0,0,0,0,0,2}

    Then SD = sqrt(8/7)

    and SD(A) > SD (B)

    So i think we need to consider 2nd Statement as well which says that

    both sets are evenly spaced sets.

    what i interpret from this statement is that difference b/w two consecutive items in both sets should be same.

    eg.

    Set A = ( -5 , -3, -1 , 1, 3) # difference of 2 b/w consecutive items

    => SD = sqrt(10)

    and

    Set B = ( -4 , -2 , 0 , 2, 4) # difference of 2 b/w consecutive items

    => SD = sqrt(8)

    SD (A) > SD (B)

    Hence Ans is C

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    Post Fri Jan 21, 2011 7:22 am
    Ramit88 wrote:
    If sets A & B have the same number of terms, is the Standard deviation of set A greater than the Standard deviation of set B ?

    1. the range of set A is greater than the range of B
    2. sets A & B are both evenly spaced sets

    ANS:C

    but i read somewhere if sets have same no. of digits then the set with higher range have greater Standard deviation .. can someone please explain this to me
    Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:

    Do the values in set A deviate more from the mean than the do values in set B?

    Let SD = standard deviation.

    Statement 1:
    We know that the distance between the biggest and smallest values in A is greater than the distance between the biggest and smallest values in B.
    But we don't know the mean, and to determine which set has a greater SD, we need to know how all the numbers in each set -- not just the biggest and smallest -- are deviating from the mean.
    Insufficient.

    Statement 2:
    When values are evenly spaced, the mean = the median, and all the values are symmetrical about the median.
    For example, if m = median, and all the values are consecutive even or odd integers, the set will look like this:

    ...m-6, m-4, m-2, m, m+2, m+4, m+6...

    But to determine which set has a greater SD, we need to know in each set the distance between each successive pair of values. For example:

    If A = consecutive even integers = {2,4,6} and B = consecutive multiples of 3 = {3,6,9}, then the values in B deviate more from the mean and B has the larger SD.
    If A = consecutive multiples of 3 = {3,6,9} and B = consecutive even integers = {2,4,6}, then the values in A deviate more from the mean and A has the larger SD.
    Insufficient.

    Statements 1 and 2:
    A and B have the same number of values.
    A and B are both evenly spaced sets, so the values in each set are symmetrical about the mean.
    The range in A is greater.
    For A to have a greater range, the distance between each successive pair in A must be greater than the distance between each successive pair in B. In other words, the values in A are more spread out.
    Thus, the values in A are deviating more from the mean, and A has a larger SD.
    Sufficient.

    The correct answer is C.

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    Post Thu Feb 10, 2011 12:10 pm
    ^^^^

    Great explanation!

    What's the source of this problem?

    giovanni.gastone Rising GMAT Star
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    Post Sat May 28, 2011 11:24 pm
    GMATGuruNY wrote:
    Ramit88 wrote:
    If sets A & B have the same number of terms, is the Standard deviation of set A greater than the Standard deviation of set B ?

    1. the range of set A is greater than the range of B
    2. sets A & B are both evenly spaced sets

    ANS:C

    but i read somewhere if sets have same no. of digits then the set with higher range have greater Standard deviation .. can someone please explain this to me
    Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:

    Do the values in set A deviate more from the mean than the do values in set B?

    Let SD = standard deviation.

    Statement 1:
    We know that the distance between the biggest and smallest values in A is greater than the distance between the biggest and smallest values in B.
    But we don't know the mean, and to determine which set has a greater SD, we need to know how all the numbers in each set -- not just the biggest and smallest -- are deviating from the mean.
    Insufficient.

    Statement 2:
    When values are evenly spaced, the mean = the median, and all the values are symmetrical about the median.
    For example, if m = median, and all the values are consecutive even or odd integers, the set will look like this:

    ...m-6, m-4, m-2, m, m+2, m+4, m+6...

    But to determine which set has a greater SD, we need to know in each set the distance between each successive pair of values. For example:

    If A = consecutive even integers = {2,4,6} and B = consecutive multiples of 3 = {3,6,9}, then the values in B deviate more from the mean and B has the larger SD.
    If A = consecutive multiples of 3 = {3,6,9} and B = consecutive even integers = {2,4,6}, then the values in A deviate more from the mean and A has the larger SD.
    Insufficient.

    Statements 1 and 2:
    A and B have the same number of values.
    A and B are both evenly spaced sets, so the values in each set are symmetrical about the mean.
    The range in A is greater.
    For A to have a greater range, the distance between each successive pair in A must be greater than the distance between each successive pair in B. In other words, the values in A are more spread out.
    Thus, the values in A are deviating more from the mean, and A has a larger SD.
    Sufficient.

    The correct answer is C.
    Really good explanation. Thank you.

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    Post Wed Apr 04, 2012 10:21 am
    S1: Std deviation is not a function of range unless it is a normal distribution which is not specifically told in the statement

    S2: At least one term of each element is required

    Comb: Can easily say which set has higher std deviation

    (C) is ans

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    anujan007 Rising GMAT Star Default Avatar
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    Post Sat Jul 21, 2012 5:46 pm
    I worked on it the way Mitch has mentioned and came down to the choice of whether the answer was C or E.

    I concluded that since there is no way to know the mean with both statements, both together are insufficient and hence chose E.

    After going through the explanation, realized my mistake. This will surely help should I face such a problem again.

    Thanks Mitch!

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    Post Mon Sep 10, 2012 4:05 am
    IMO C, @ 10 sec

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    Post Mon Sep 10, 2012 4:05 am
    IMO C, @ 10 sec

    eski Rising GMAT Star Default Avatar
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    Post Tue Sep 18, 2012 12:48 pm
    I have a question, my take home is

    to get SD only 2 parameters imp?
    1. mean
    2. spread that can be range , indivual values, etc

    am i correct?

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    Post Sun Apr 21, 2013 6:08 am
    D

    when the number of terms are same the set with greater range has greater deviation.

    for sets with even spaced elements the deviation is same.

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