Data Sufficiency

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.

The OA is the option A.

This kind of questions are difficult for me. Experts, may you explain to me how to solve this DS question? Please.

M7MBA 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.

The OA is the option A.

This kind of questions are difficult for me. Experts, may you explain to me how to solve this DS question? Please.

CONCEPT:
The standard deviation depends on two things
1) The Deviation among the terms when terms are arranged in ascending/descending order
2) Number of terms in the set

Question: What is the standard deviation of a set of consecutive integers?
We already know the deviation among the terms as the terms in set are consecutive
therefore we only need to know the number of terms in teh set

Statement 1: Set Q contains 21 Integers

SUFFICIENT

Statement 2: Median of Set Q is 20

But this doesn't help us with the number of terms in set Q hence

NOT SUFFICIENT

Answer:" option A

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.

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.