Comparing Standard Deviations

[getneonow]

CLASS -> AVG AGE -> NO. OF STUDENTS

A -> 15-> 6

B -> 16 -> 12

Is the standard deviation of ages of students in class A greater than that of class B ?

1) The difference between ages of any two students in class A is always more than 1 yr.

2) No student in class B is more than 6 months older than any other student.[/list]

[Stuart@KaplanGMAT]

CLASS -> AVG AGE -> NO. OF STUDENTS

A -> 15-> 6

B -> 16 -> 12

Is the standard deviation of ages of students in class A greater than that of class B ?

1) The difference between ages of any two students in class A is always more than 1 yr.

2) No student in class B is more than 6 months older than any other student.

Even if you don't understand standard deviation, you should quickly be able to eliminate choices A, B and D, since clearly neither statement is sufficient alone (each statement only gives info on 1 of the 2 classes; we need info on both to solve).

So, let's chat about the question, then jump directly to combining the statements.

Standard deviation is the measure of how spread out the numbers in a set are from the mean: the greater the spread from the mean, the higher the standard deviation of the set.

To calculate the SD of a set (which you'll never need to do on the GMAT, so you definitely don't need to know the formula), you need to know two things about the set:

1) the number of terms; and
2) the exact spacing of all of the terms.

In this question we don't need to actually calculate the SD of either set - we merely need enough information to compare the two SDs.

On to the statements!

1) each term in the set is more than 1 unit apart from the number below it and the number above it.

2) the maximum range of class B is .5 units.

(1 unit = 1 year)

Based on (1), we know that class A contains 6 students and a range greater than 5; based on (2) we know that class B contains 12 students and a range less than .5. Accordingly, class B is packed much tighter around the mean and has a considerably lower SD than class A. Sufficient, choose (C).

[pnk]

To calculate the SD of a set (which you'll never need to do on the GMAT, so you definitely don't need to know the formula), you need to know two things about the set:

1) the number of terms; and
2) the exact spacing of all of the terms.

Thanks Stuart. You explained it very nicely.

Just one doubt, to find whose SD is greater btn 2 sets - do we need to know nos of items also. I feel, if we know spread of 2 sets, we can understand SD is greater for which set. In other words, range of 2 sets will be sufficient to understand whose SD is greater.

Is that a correct understanding? Pls help

[Stuart@KaplanGMAT]

To calculate the SD of a set (which you'll never need to do on the GMAT, so you definitely don't need to know the formula), you need to know two things about the set:

1) the number of terms; and
2) the exact spacing of all of the terms.

Thanks Stuart. You explained it very nicely.

Just one doubt, to find whose SD is greater btn 2 sets - do we need to know nos of items also. I feel, if we know spread of 2 sets, we can understand SD is greater for which set. In other words, range of 2 sets will be sufficient to understand whose SD is greater.

Is that a correct understanding? Pls help

Hi,

just the range isn't enough to calculate SD - you need to know the spacing between every pair of terms. You can have sets with outliers that have very low SD.

For example,

{1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 50}

will have a lower SD than:

{1, 40}

even though the first set has a bigger range.