TestMagic

Jeanette · 07-02-2008, 09:18 PM

If you see two groups of numbers, and one group has a wider spread than the other, can you automatically assume that it has a greater standard dev? Or is there something else to look out for?

For example, the numbers 8,10,12,14,16 have a greater standard dev than 8,9,10,10,11,12.

Can you think of examples that break this rule?

Goldust · 07-03-2008, 03:09 AM

I would think that the SD depends on the spread as well as the number of terms. I can't think of any example though.

Jeanette · 07-03-2008, 03:16 AM

So if you have 50 numbers with a spread of 1 to 50, it has a greater standard dev than 60 numbers with a spread of 1 to 50?

chestnut.cc · 07-03-2008, 06:03 AM

Standard deviation is deviation from the mean... it is the ROOT of the AVERAGE of the SUM of the SQUARE of the DIFFERENCE betn each observation and the MEAN of the data...

Now we fortunately dont have to apply it like that... but what sd measures is the AVERAGE SPREAD OF THE DATA FROM THE MEAN... if you can visualize a cloud of data clustered around a line representing the mean value... then sd gives us the uniform width both above and below that line... As it is an average... larger spreads do not necessarily indicate larger sd... by spread i assume you mean the diff betn the largest and smallest observation... it is more dependant on the no of observations... It also means we can approximate sd as the average of the spread from the mean...

NOTE: only the absolute diff betn the observation and the mean are to be taken... so the diff betn 2 and mean 4 isnt -2 its 2...

Consider the 2 sets of observations
1 2 3 4 4 10... spread from mean... 3 2 1 0 0 6... average spread = 2

1 1 1 3 4 7 7 4... spread from mean... 3 3 3 1 0 3 3 0... average spread = 2.57

clearly the spread is greater in the second case even though the cloud is more compact...

KBTA · 07-03-2008, 06:03 AM

IMO

The 2nd group has more numbers (in quantity) with lesser difference betn numbers. So, the first group has higher standard deviation.

econ_phd_2009 · 07-03-2008, 06:45 AM

Quote:

Originally Posted by Jeanette

So if you have 50 numbers with a spread of 1 to 50, it has a greater standard dev than 60 numbers with a spread of 1 to 50?

excuse me, I didn't understand your wording. Please make it clear.

geek_goddess · 07-03-2008, 06:33 PM

You have to see the spread wrt the mean. Why would it depend on the number of terms ? If you just took more values at equal distances around the mean, they'd cancel each other out.
I always make the mistake of seeing how far the numbers are from each other, rather than from their average.
there is a question in the pp quant comp set which explained this well, and corrected my error.

Jeanette · 07-03-2008, 06:48 PM

Quote:

Originally Posted by econ_phd_2009

excuse me, I didn't understand your wording. Please make it clear.

Let's say you have 60 numbers, with a range of 1 to 50.

You are comparing it to a set of 50 numbers, with a range of 1 to 50.

Does the set of 50 numbers have a higher or lower standard dev than the set of 60? Or there's no way to tell without knowing the particular numbers?

chestnut.cc · 07-03-2008, 07:24 PM

eeps... bbcode... :s

chestnut.cc · 07-03-2008, 07:25 PM

Quote:

You have to see the spread wrt the mean. Why would it depend on the number of terms ? If you just took more values at equal distances around the mean, they'd cancel each other out.

Wrong... sd is intended to reflect the deviation around the mean... a simple average of deviation from mean would mean they cancel out... but sd is the square of the diff from mean...

Quote:

Does the set of 50 numbers have a higher or lower standard dev than the set of 60? Or there's no way to tell without knowing the particular numbers?

Refer my previous post... :s

07-02-2008, 09:18 PM	#1 (permalink)
Jeanette Got it Join Date: Jun 2008 Posts: 126	Standard Dev shortcut If you see two groups of numbers, and one group has a wider spread than the other, can you automatically assume that it has a greater standard dev? Or is there something else to look out for? For example, the numbers 8,10,12,14,16 have a greater standard dev than 8,9,10,10,11,12. Can you think of examples that break this rule?

07-03-2008, 06:03 AM	#5 (permalink)
KBTA TestMagic Guru-in-Training Join Date: Jun 2007 Location: Joypurhat, Bangladesh Posts: 566	IMO The 2nd group has more numbers (in quantity) with lesser difference betn numbers. So, the first group has higher standard deviation. _ _ _ _ SIG _ _ _ _ Rgds, Jakir

Thread Tools	Search this Thread
Show Printable Version Email this Page	Search this Thread: Advanced Search
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

07-03-2008, 03:09 AM	#2 (permalink)
Goldust Let's get it on Join Date: May 2008 Location: India Posts: 333	I would think that the SD depends on the spread as well as the number of terms. I can't think of any example though.

07-03-2008, 03:16 AM	#3 (permalink)
Jeanette Got it Join Date: Jun 2008 Posts: 126	So if you have 50 numbers with a spread of 1 to 50, it has a greater standard dev than 60 numbers with a spread of 1 to 50?

07-03-2008, 06:03 AM	#4 (permalink)
chestnut.cc Wouldbegood... Join Date: Jun 2008 Posts: 273	Standard deviation is deviation from the mean... it is the ROOT of the AVERAGE of the SUM of the SQUARE of the DIFFERENCE betn each observation and the MEAN of the data... Now we fortunately dont have to apply it like that... but what sd measures is the AVERAGE SPREAD OF THE DATA FROM THE MEAN... if you can visualize a cloud of data clustered around a line representing the mean value... then sd gives us the uniform width both above and below that line... As it is an average... larger spreads do not necessarily indicate larger sd... by spread i assume you mean the diff betn the largest and smallest observation... it is more dependant on the no of observations... It also means we can approximate sd as the average of the spread from the mean... NOTE: only the absolute diff betn the observation and the mean are to be taken... so the diff betn 2 and mean 4 isnt -2 its 2... Consider the 2 sets of observations 1 2 3 4 4 10... spread from mean... 3 2 1 0 0 6... average spread = 2 1 1 1 3 4 7 7 4... spread from mean... 3 3 3 1 0 3 3 0... average spread = 2.57 clearly the spread is greater in the second case even though the cloud is more compact...

07-03-2008, 06:33 PM	#7 (permalink)
geek_goddess Eager! Join Date: Jun 2008 Posts: 79	You have to see the spread wrt the mean. Why would it depend on the number of terms ? If you just took more values at equal distances around the mean, they'd cancel each other out. I always make the mistake of seeing how far the numbers are from each other, rather than from their average. there is a question in the pp quant comp set which explained this well, and corrected my error.

07-03-2008, 07:24 PM	#9 (permalink)
chestnut.cc Wouldbegood... Join Date: Jun 2008 Posts: 273	eeps... bbcode... :s

TestMagic

Free GMAT, GRE, SAT Test, TOEFL practice tests