What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) Q has 20 members
A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D) Each statement alone is sufficient to answer the question.
E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.
E
E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.
Hi,
Guess its E, as the set is not defined and hence in calculable.. Admin please help.
Many Thanks
D
d
D
The standard deviation should be the same
D)
d
it should be D
D
Explanation:
The question says that they are consecutive numbers.
1) 21 items, the average is the item number 11. 10 items before the average and 10 items after it. Think about it as distances; the distance of every item from the average is equal from the 2 sides of the average. So the standard deviation is zero.
2) 20 Items, the average is the average of item 10 and item 11, in the same we as we have just explained in previous one, we will ge that the standard deviation is zero also.
So it is D.
I agree with Wael’s answer but the explanation is incorrect. The std-dev is not zero. You square the differences when calculating std-dev and so std-dev could never be zero unless all numbers arethe same.
Well, the standard deviation won’ be the same for an even number of data points and an odd number of data points (sequential).
The std. dev. will be the same for all sets with an odd number of data points that are sequential
The same can be said for all sets with an even number of data points that are sequential.
These two values do not equal each other though. Think of it. The “distance” from center is different. In an odd number set (going in either direction) it will be 1, 2, 3, 4, etc etc….e.g., median is 4, next point is 5 (4+1), then 6 (4+2), etc etc. In an even number set, the distances are 0.5, 1.5, 2.5, etc etc, so the std dev values will differ.
Each statement will allow you to calculate a standard deviation, but they will be different from each other.
The even number set is because…the median is not the mean, unlike in an odd number set…
here i obviously mean even number = even number of data points
E
since set of consecutive intergers menas we donno whether it is positive or
negative and consecutive may be from -2 or -1 0r from 51 or 100 we cannot say so E is the answer
E
OA is a
My apologies the ans is D.
the question i compared this with had a different ans choice for B.
D
D:
answer is D
E:
Option E
TakeGMAT answer please
Official Answer is D.
option D
D.
According the formulae for S.D. : S.D. = sqrt{1/n(Summation of squares of the differences of mean and each number)}.
n= no. of items in the sample space.
Now suppose we have a sequence of five numbers: 5,6,7,8,9.
Mean: 7
n = 5
S.D. = sqrt[1/5{(5-7)^2 +(6-7)^2 + (7-7)^2 + (8-7)^2 + (9-7)^2}]
= sqrt[1/5{4+1+0+1+4}]
= sqrt[10/5]
= sqrt(2).
Now if we increase the sample space by say two more elements.
So the sequence is: 4,5,6,7,8,9,10
Mean = 7
n = 7
S.D. = sqrt[1/7{(4-7)^2 + (5-7)^2 +(6-7)^2 + (7-7)^2 + (8-7)^2 + (9-7)^2 + (10-7)^2 }]
= sqrt[1/5{(9+4+1+0+1+4+9}]
= sqrt[28/7]
= sqrt(4)
= 2.
Hence, the standard deviation is dependent on the sample set that we take. So unless we know all th elements in the sample set we cannot say anything about the Standard deviation.
Ans: E
Sorry Guys..
Misunderstood the question.
Ans would be D…
D