A certain list of 100 data has an average of 6 and standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list,must result in a list of 102 data with standard deviation less than d?
A) -6 and 0
b) 0 and 0
c) 0 and 6
d) 0 and 12
e) 6 and 6

Please can you help me giving some theory on standard deviation as well. I am bit weak in SD. It always keep my score low in GMAT.

Thanks
r.

Hi,

Please can you help me with one more from GMAT Prep.Its a DS question.

If x-y>10, is x-y>x+y
1)x=8
2)y=-20


Will be really greatful, I am writing my exam on 8th Apr.

Thanks
r.

First Question: It's important to remember that standard deviation is a measure of how dispersed the data in the set is. The smaller the standard deviation, the more clustered the data is around the mean. The larger the standard deviation, the more dispersed the data is from the mean. The question tells us that the mean is 6 and wants us to select the two values that would effectively decrease the standard deviation. It's important to recognize that we don't know what the hundred numbers are. Also, since the question tells us that 'd' is positive, we know for a fact that the numbers aren't all 6 (which would give us a SD of 0).

The correct answer should be E. Adding two 6's to the data set would keep the mean constant and would guarantee that the SD is reduced because it would effectively increase the closeness of the data set to the mean.

Think about a smaller example. Say the data set is 0, 6, 12. The mean is 6 and adding two 6's to this data set would increase the closeness of the data set to the mean and thus reduce the SD.

All the other answer choices either effect the value of the mean or are not guaranteed to increase the closeness of the data set.

Second Question:

(1) SUFFICIENT. If x=8, then we know y < -2. Since y is guaranteed to be negative, we know for a fact that x-y > 8 and x+y < 8. We can definitely say that x-y > x+y. Note that if we think about this in terms of a number line, if y is negative then the value of x-y is to the right of x and the value of x+y is to the left of x.
(2) SUFFICIENT. Since y is guaranteed to be negative, the value of x-y is to the right of x on a number line and the value of x+y is to the left of x on a number line. Therefore, we can definitely say that x-y > x+y.

The correct answer should be D.

Hi,

Thanks a lot for the explanations for both the answers. It really helps. And to know the basic of SD is really nice. Thanks for your help.


Ta
r.

As for your other question:

If x-y>10, is x-y>x+y?
1)x=8
2)y=-20

First, manipulate the second equation.
If x-y>x+y, then we can subtract x from both sides and add y to both sides and get:
0>2y
Then divide by 2, and our question becomes whether y is negative.
(Remember, we CANNOT divide or multiply an inequality by a variable, since we don't know whether the variable is positive or negative, or even 0.)

Now, look at statement 1.
x=8
Thus, 8-y>10
8>y+10
-2>y
This tells us that y is negative, which is all we need to know.

Statement 2.
y=-20
Obviously this one is enough, as it also tells us that y is negative.

Thus, the answer should be D.

Hope this helps,

Veritas Help