You can pick numbers to create an example, but that will take too long.
But all you have to understand is the logic of standard deviation.
what does standard deviation tell you? how does it fluctuate? The further the number is, the greater standard deviation is.
for example, if you have 2,2,2,9 vs. 2,2,2,2, the standard deviation is much bigger with 2,2,2,9. so far so good?
so now, let's read the problem.
The standard deviation = d
100 data.. ok.. blah blah
average = 6
now, we're going to add two more data...
just think of it as, by adding these two, I'm closing the gap, so anything closer to the average will close that gap. 6 and 6 will make that happen.
I hope you understand my explanation.
I found out that on GMAT, you need to understand the SD, not know the formula. You'll most likely not solve one, but to use the logic.
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standard deviation
Source: Beat The GMAT — Problem Solving |
Another way to look at SD, thanks to lunarpower(ron), is to remember SD as the distance from the numbers in the set to the mean.
So in your question, the mean=6, and the question asks which two additional numbers will result in a SD that's less than d.
so looking at the choices
A.) -6 and 0, will have an SD of 12 and 6, respectively
B.) 0 and 0, will have an SD of 6 and 6, respectively
C.) 0 and 6, will have an SD of 6 and 0, respectively
D.) 0 and 12, will have an SD of 6 and 6, respectively
E.) 6 and 6, will have an SD of 0, and 0, respectively
hence, E. The addition of 6 and 6, should be lower than d (or as hwiya320 mentioned, "close the gap"), because 6 is the same as the mean, resulting in a SD that is equal to 0.
So in your question, the mean=6, and the question asks which two additional numbers will result in a SD that's less than d.
so looking at the choices
A.) -6 and 0, will have an SD of 12 and 6, respectively
B.) 0 and 0, will have an SD of 6 and 6, respectively
C.) 0 and 6, will have an SD of 6 and 0, respectively
D.) 0 and 12, will have an SD of 6 and 6, respectively
E.) 6 and 6, will have an SD of 0, and 0, respectively
hence, E. The addition of 6 and 6, should be lower than d (or as hwiya320 mentioned, "close the gap"), because 6 is the same as the mean, resulting in a SD that is equal to 0.
