B?

Range/2 > SD.

Since SD is 500, Range must be greater than 500.

iamjakekim wrote:B?

Range/2 > SD.

Since SD is 500, Range must be greater than 500.

Can you please tell more abt this rule i.e. how the relation between SD and range exist ? I am not able to find relation between range and standard deviation.

As per my understanding SD is calculated as below:

1. Let's say there are N numbers.
2. Take the mean of numbers.
3. Subtract every number from the mean.
4. Square every number that we received in step 3.
5. Add all the numbers that we get in step 4.
6. Take the average of the number that we get in step 5.
7. Take the positive square root of the number that we get in step 6.
8. standard deviation is the number that we get in step 7 above.

For e.g. let say's numbers are 1, 2, 3. Thus the above steps become:

1. N = 3.
2. Mean = 2.
3. subtracting we get (1, 0, -1)
4. squaring we get (1, 0, 1)
5. Adding = 1 + 0 + 1 = 2.
6. Average = 2/3
7. square root = (2/3)^(1/2)
8. Standard deviation = (2/3)^(1/2)

But in the above calculation looks like there is no relation between range and standard deviation.

Please tell what I am missing here.

I am pretty sure there is a relation ship between R and SD.

However, I am not an expert. I just memorized that R/2 > SD.

Median and Mean has no relationship. <--- This one as well.

You jsut memorize it.

Hi,

I couldnt figure out a connection between the two..
pls explain.

Thanks,

SD is always less than the range

mehravikas wrote:SD is always less than the range

Can you please tell why ?

iamjakekim wrote:I am pretty sure there is a relation ship between R and SD.

However, I am not an expert. I just memorized that R/2 > SD.

Median and Mean has no relationship. <--- This one as well.

You jsut memorize it.

Hi iamjakekim,

IMO there is a relation between mean and median....for a AP set....

when the difference between numbers is fixed, then in that mean = median. But the converse is not true...i.e. if mean = median for a given set then it does not mean that numbers are in AP.

I am not aware of any other relation between mean and median except the above one.

Thanks
Mohit

I have to search for a GMAT Prep question for this...its on this forum !!

goelmohit2002 wrote:

mehravikas wrote:SD is always less than the range

Can you please tell why ?

mehravikas wrote:I have to search for a GMAT Prep question for this...its on this forum !!

goelmohit2002 wrote:

mehravikas wrote:SD is always less than the range

Can you please tell why ?

Can you please help.....because I am not aware of any relation that exist between Range and standard deviation....except that when Range = 0, then standard deviation = 0.

my pick is standard deviation is less than the range but how much less cannot determine unless we have the complete set of numbers.

Unfortunately, I am not able to find that post. But I do remember it because as soon as I read it I added it to my notes.

We can ask some great minds on this forum. I hope you are aware of other rules of standard deviation such as.

1. If you add, subtract the set of numbers by a constant then the SD doesn't change
2. If you multiply SD will change

goelmohit2002 wrote:

mehravikas wrote:I have to search for a GMAT Prep question for this...its on this forum !!

goelmohit2002 wrote:

mehravikas wrote:SD is always less than the range

Can you please tell why ?

Can you please help.....because I am not aware of any relation that exist between Range and standard deviation....except that when Range = 0, then standard deviation = 0.

mehravikas wrote:my pick is standard deviation is less than the range but how much less cannot determine unless we have the complete set of numbers.

Unfortunately, I am not able to find that post. But I do remember it because as soon as I read it I added it to my notes.

We can ask some great minds on this forum. I hope you are aware of other rules of standard deviation such as.

1. If you add, subtract the set of numbers by a constant then the SD doesn't change
2. If you multiply SD will change

Yes, I am aware of the other rules...thanks for refreshing the same in my memory....

but can you please tell why SD should be less than range ? Any mathematical reason ?

Just searched on the net too...I am not able to find any such relationship....

https://www.socialresearchmethods.net/kb/statdesc.php

For e.g. The above link details how to calculate the SD etc...but does not tell any link between them

I'm sure that I saw it on this forum...

goelmohit2002 wrote:Just searched on the net too...I am not able to find any such relationship....

https://www.socialresearchmethods.net/kb/statdesc.php

For e.g. The above link details how to calculate the SD etc...but does not tell any link between them

The formula for range is R = xn - x1 (greatest value of set - smallest value of set).

The formula for standard deviation is... pretty long and hard to explain. All you should remember here is that the standard deviation is the average distance from the mean of the set to the set's components.

So you know the following:
- R = distance from greatest to smallest (basically longest distance in set)
- SD = average distance from mean (which is somewhere in the middle) to an element of the set

As you can probably guess from the above, R will always be greater than SD. I'm not sure if indeed R/2 > SD and I'm not even going to go as far as to pretend I want to try to demonstrate it, seen as how the formula for SD is impossibly long and convoluted (general case of n elements in set).

However, if you remember that R > SD, it will be more than enough to solve the problem at hand.

Edit: After some philosophical 3 a.m. thinking, the R/2 > SD formula may not be that hard to demonstrate. Will try maybe tomorrow.