Is the standard deviation of set S greater than the standard

Question

Is the standard deviation of set S greater than the standard deviation of set T?

1. The range of set S is greater than the range of set T
 2. The mean of set S is greater than the mean of set T

FN · Answer

i think its A..

range means smallest value and largest value are further apart in S..so based on that alone SD is going to be higher..

kman · Answer

Agree with A. Bigger range = data points farther apart, means higher SD.

2 --> Insuff. Bigger mean does not lead to bigger SD

LiveStronger · Answer

E

stmt1:
{2,4,6,8,10,12} - SD =2,Range-10
{1,3,5,7,9} - SD =2, Range-8

{1,4,7,10} - SD =3,Range-9
{1,3,5,7,9} - SD =2, Range-8
InSuff

stmt2:
{2,4,6,8,10,12} - SD =2, Mean is 7
{1,3,5,7,9,11} - SD =2, Mean is 6

{2,6,10,14,18} - SD =4, Mean is 10
{1,3,5,7,9,11} - SD =2, Mean is 6
InSuff

Together:
{2,6,10,14,18} - SD =4, Mean is 8, Range is 16
{1,3,5,7,9,11} - SD =2, Mean is 6, Range is 10

{2,4,6,8,10,12,14} - SD =2, Mean is 8, Range is 12
{1,3,5,7,9} - SD =2, Mean is 5, Range is 8
InSuff

I definitely won't be solving this problem in such detail, but thought would put different examples together

amitdgr · Answer

OA is E <img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" />

kman · Answer

Just when I thought I had figured out SD problems.

Guys, Can you help me to understand this conceptually. Range only depends on two points. Is that the reason we cannot use the range to estimate an SD? What information would have helped to answer this DS question?

GMAT TIGER · Answer

1: Small range with equal number of elements in the sets tells us that the set with smaller range is smaller SD and vice versa but ranges without the number of elements in sets do not tell us which set has larger SD and vice versa.

2: Means alone donot tell us anything about SDs.

Togather: NSF.

Set S: 10, 14, 15, 15, 15, 15, 15, 15, 15, and 21
Range = 11
Mean = 15
SD = 2.624669291 (using excel sheet - just for demonestrating purpose)

Set T: 5 and 15
Range = 10
Mean = 10
SD = 7.071067812 (using excel sheet - just for demonestrating purpose)

Therefore E.

scthakur · Answer

You are right. Range is only the difference between the highest and lowest value in the set. However, standard deviation is the distance from the mean (remember normal distribution curve).

Another important aspect is to know that standard deviation is relative to the mean. What this means is that even if the absolute mean is higher, standard deviation can be smaller.

With these, it is clear that answer should be E.

Is the standard deviation of set S greater than the standard

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