If Q is a set of consecutive integers, what is the standard

Question

If Q is a set of consecutive integers, what is the standard deviation of Q?

(1) Set Q contains 21 terms.

(2) The median of set Q is 20.

fivedaysleft · Answer

st 2. median = 20
set = {19,20,21} or set = {18,19,20,21,22} => different deviations...so not sufficient

st 1 : set has 21 elements...so my median = mean = a22/2 = a11

for deviation formula is (sum of|ai-mean|)/n

here we know n=21
mean = a10
since they are consecutive integers |a1-a2|=1
so we |a11-a1|=10 similiarly all deciations can be found...squared and divided...so we will get a proper answer...therefore statement 1 is conclusive and sufficient!

hope it helps

also, study the Gmatclub notes on standard deviation in Gmat book

ruturaj · Answer

please let me know the link for standard deviation probs

Posted from my mobile device

fivedaysleft · Answer

gmatclub(dot)com/forum/gmat-math-book-87417(dot)html

i have placed unwanted (dot)s in between cuz i cant post links...havent been a member for five days...but thats the address for the open source book....go to the standard deviation section...very nice...all inclusive...you wont need to refer a second source.

IanStewart · Answer

If you know all of the distances within a set, you can always find its standard deviation, since standard deviation is only based on the distances from each element to the average. So if you have a set of 21 consecutive integers, you can always find the standard deviation; you don't need to know how big these integers are.

If it's not clear why that's true, you can let M be the average of your 21 consecutive integers (M is also the median since our set is equally spaced). Then your set is:

M-10, M-9, M-8, ..., M-1, M, M+1, ..., M+8, M+9, M+10

and you can see that we know all of the distances from each element to M; those distances are 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Those are the numbers you need to compute standard deviation.

harshavmrg · Answer

fivedaysleft,

Can you please explain statement1 again?
mean = a22/2 = a11

When is your GMAT? is it over?

fivedaysleft · Answer

it means that in an ordered set the mean is always the middle number
ie for a set with 21 elements, the middle element is the (21+1)/2 element ie a11

my GMAT was today.
got shredded in verbal. 34
quants was decent 48
680 in all

IanStewart · Answer

You mean to say that in an 'equally spaced' set, the mean and median are equal. There's no such thing as an 'ordered set'; sets are not in any order (if a list of numbers is in order, it's a sequence, not a set).

Chetangupta · Answer

Statement 1) sufficient, 21 terms known, stdev can be found (no need to calculate)
Statement 2) no of terms not known, not sufficient

A

fivedaysleft · Answer

acknowledged. My bad

vinayreguri · Answer

To find SD we need Set where we can find mean and then calculate SD

So A is sufficient. B has no relation with median

thinkvision · Answer

The procedure for finding the standard deviation for a set is as follows:
 
1) Find the difference between each term in the set and the mean of the set.
 
2) Average the squared "differences."
 
3) Take the square root of that average.
 
Notice that the standard deviation hinges on step 1: finding the difference between each term in the set and the mean of the set. Once this is done, the remaining steps are just calculations based on these "differences."
 
Thus, we can rephrase the question as follows: "What is the difference between each term in the set and the mean of the set?"
 
(1) SUFFICIENT: From the question, we know that Q is a set of consecutive integers. Statement 1 tells us that there are 21 terms in the set. Since, in any consecutive set with an odd number of terms, the middle value is the mean of the set, we can represent the set as 10 terms on either side of the middle term x:

Notice that the difference between the mean ( x) and the first term in the set ( x – 10) is 10. The difference between the mean ( x) and the second term in the set ( x – 9) is 9. As you can see, we can actually find the difference between each term in the set and the mean of the set without knowing the specific value of each term in the set!
 
(The only reason we are able to do this is because we know that the set abides by a specified consecutive pattern and because we are told the number of terms in this set.) Since we are able to find the "differences," we can use these to calculate the standard deviation of the set. Although you do not need to do this, here is the actual calculation:
 
Sum of the squared differences:
102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12 + 02 + (-1)2 + (-2)2 + (-3)2 + (-4)2 + (-5)2 + (-6)2+ (-7)2 + (-8)2 + (-9)2 + (-10)2 = 770
 
Average of the sum of the squared differences: 
770

21
 = 36 
2

3

The square root of this average is the standard deviation: ≈ 6.06
 
(2) NOT SUFFICIENT: Since the set is consecutive, we know that the median is equal to the mean. Thus, we know that the mean is 20. However, we do not know how big the set is so we cannot identify the difference between each term and the mean.
 
Therefore, the correct answer is A.

sham264 · Answer

Can anyone please help me understanding where am I making the mistake:

From condition 2, we know that the median is 20 and we also know that the series is composed of consecutive integers. I will assume that the series is from 1 to n because my understanding is that no matter where the series of consecutive integers starts from, as long as we know the number of elements in the series we can find SD. And also here mean = median.

= 20
n=39

Hence with n known, we can calculate SD. So I believe condition 2 is sufficient too. Can someone please help me with understanding what am I missing?

Thanks in advance!

Bunuel

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If Q is a set of consecutive integers, what is the standard

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If Q is a set of consecutive integers, what is the standard

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