Mean/Median/Standard Deviation quick question

Bunuel has already posted links to various sets related theory.

For the sake of completeness, below are the answers for your questions:

1. If each number in a group of numbers is increased by the same constant AMOUNT, how does the mean, median and standard deviation change?

Mean will become = Old mean + Amount ,

You can look at it like this:

Lets say your original mean = M = Sum of all the elements / n ---> M =S/n . Now when you add a fixed amount (say 'a') to all the elements, the new sum becomes: S+n*a and the new average becomes: Mn (new average) = (S+na)/n = S/n + a = M +a .

Thus the mean changes to old mean + AMOUNT.

ii) Median will be increased by 'a'

Median is the center most term and as you are adding a CONSTANT AMOUNT , all the elements will be 'shifted' by 'a' and hence the middle most term will become OLD MEDIAN + a

Thus NEW MEDIAN = OLD MEDIAN + a

iii) Standard deviation

Here are the rules for SD:

SD_new = SD_old (when you add or subtract a value 'a')

SD_new = SD_old / a or SD_old *a (when you divide or multiply by a value 'a')

2. Also, if each number in a group of numbers is increased by the same constant PERCENTAGE, how does the mean, median and standard deviation change please?

A percentage can be treated as an additional number 'a' multiplied to the original elements. LEts say you have a set : {1,2,3} and then you increase all by 10% ---> In effect, you are multiplying ALL the elements by 1.1.

Thus based on rules mentioned in (1)

Mean_new = Mean_old * a .

Look at it this way:

Lets say your Mean_old = Sum / n ---> Sum_new with all elements multiplied by a (can be integer or fraction) = Sum_old * a ---> Mean_new = Sum_new / n = Sum_old * a /n = Mean_old*a

Median_new = Median_old * a (as Median is only the middle most value of an ordered set!).

Finally, SD_new = SD_old / a or SD_old *a

Hope this helps.

All the best for your GMAT.