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.
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standard deviation
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j_shreyans
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Target question: What is the standard deviation of Q?j_shreyans wrote: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.
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Given: Q is a set of CONSECUTIVE integers
Statement 1: Set Q contains 21 terms.
NOTE: Standard Deviation measures dispersion (spread-apart-ness). As such, the actual values mean nothing compared to RELATIVE values.
For example, the set {1,2,3,4} has the SAME STANDARD DEVIATION as the set {6,7,8,9}
So, knowing that set Q consists of 21 CONSECUTIVE integers is SUFFICIENT.
The Standard Deviation of Q will be the same as the Standard Deviation of {1,2,3,4...20,21}
Statement 2: The median of set Q is 20.
There are several different sets that satisfy this condition.
For example, set Q could equal {19, 20, 21} or set Q could equal {18, 19, 20, 21, 22}
These two sets have DIFFERENT standard deviations.
So, statement 2 is NOT SUFFICIENT
Answer = A
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SD describes how much a set of data DEVIATES from the mean.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.
For any set of of consecutive integers, the mean = the median.
Question rephrased: How do the integers in set Q deviate from the median?
Statement 1: Set Q contains 21 terms.
Any set of 21 consecutive integers will deviate from the median EXACTLY THE SAME WAY.
If M = the median, the set will look like this:
M-10, M-9...M-2, M-1, M, M+1, M+2...M+9, M+10.
Thus, the SD can be determined.
SUFFICIENT.
Statement 2: Median = 20.
If there are only 3 terms -- if Q = {19, 20, 21} -- then there is very little deviation from the median.
If there are 101 terms, then there will be quite a bit of deviation from the median.
Thus, the SD can be different values.
INSUFFICIENT.
The correct answer is A.
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As a tutor, I don't simply teach you how I would approach problems.
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