Asac123 wrote:
Is nt there something like The highest std in a set will be something with the highest range. In that case isnt E the answer ? I know the Std will anyway be less in E . But how come this theory is contradicting. Bunuel i used the same logic that u had given for ur statistics qns in ur signature. Kindly explain. !!!
Dear
Asac123,
I'm happy to respond. :-)
Please read this post:
Standard Deviation on the GMATGive particular attention to the section "Rough and ready facts about standard deviation."
For this question, (B) & (E) both have a range of 20, a larger range than the others, so let's eliminate the other three and discuss these two.
Standard deviation is, we might say, a measure of the "typical" distance between the data points in a set and the mean of the set.
In (E), the mean is 60. Two of the data points are at 60, so they have a deviation of zero, and two are 10 away from 60, so they have deviations of +10 and -10. The set of deviations is {-10, 0, 0, 10}. Ignoring positive/negative, what's the typical size of those four numbers? Hard to say. It would be something between 0 and 10.
Now, look at (B). The mean is 20, and every single data point is exactly a distance of 10 from this mean of 20. If every data point is the same distance from the mean, that distance has to be the S.D. For (B), S.D. = 10.
Since the S.D. of (B) is equal to 10 and the S.D. of (E) would be less than 10, we know that (B) has to have the biggest.
Suppose we want the exact value of the S.D. of (E). This is more than you need to know for the GMAT, but what you would do is square those deviations, add them up, average those squared values, and then take a square root of that average.
list of deviations = {-10, 0, 0, 10}
list of squared deviations = {100, 0, 0, 100}
average of squared deviations = 50
\(S.D. = \sigma = \sqrt{50} = 5\sqrt{2} = 7.071\)
Does all this make sense?
Mike :-)
Thanks Mike i understand that but if we take the range concept then wouldnt E be the answer