tejaswini0712 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.
OA A
SD describes how much a set of data DEVIATES from the mean.
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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