GMAT Prep Test Question 1 - Standard Deviation

[moshema]

A certain list of 100 data has an average (arithmetic mean) of 6 and a standard deviation of d, where d is positive. Which of the pairs, when added to the list, must result in a list of 102 data with standard diviation of less than d

a) -6 and 0

b) 0 and 0

c) 0 and 6

d) 0 and 12

e) 6 and 6

Can someone crack this for me. It was my first GMAT question and it through me off-guard that the rest of my exam was spoilt!

[druski]

I would imagine it would be option E) 6 & 6.

if you had a set of 5 numbers (1,2,3,4,5) the mean would be 3, and the standard deviation would be the sqrt of 2, or roughly 1.4. If you added two data points, both equal to the mean, the set would become 1,2,3,3,3,4,5, the mean would be 3 still, but the standard deviation would now be the sqrt of 10/7, or roughly 1.19.

Basically, adding more data points that are equal to the mean decreases the standard deviation, which makes sense. To use probably wholy incorrect math lingo, you could say the more points equal to the mean the less the average (standard) difference (deviation) from the mean is.

Any other number would increase or maintain the current standard deviation as the number would be greater/less than the mean.

[MBAorBust]

Agreed. E is the answer because standard deviation is a measure of the distance away from the mean essentially. So if you add two numbers that don't deviate from the mean, the standard deviation will go down for the set of numbers.