Can someone please explain the relation between arithmetic mean, variance and standard deviation, with examples. Thanks.
Does range come into picture here at all.
"Arithmetic mean" is synonomous with "average".
"Variance" is indeed the square of the "standard deviation". What is important to know in the GMAT is that these two numbers describe the "variability" of a group of numbers, i.e., how far apart they are scattered about their average. You will never be asked to compute a standard deviation, but you may be asked, given two groups of number, to identify which of the two has the larger standard deviation.
"Range" is simply the difference between the largest number and smallest number is a set. In general, the group with the larger range will have a larger standand deviation (but not always -- for example a group with the vast majority of its member near or at the mean with only two outliers than define the range).
In addition, you need to knwo what the "median" is. The median is the "middle" number is a group consisting of an odd number of numbers, and the average of the two middle numbers if there are an even number of numbers.
Hope this helps.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993