Standard deviation is one of the favorite topic of test makers for 45+ scorers. There are 6-7 concepts tested in this topic itself. It will help to put them at one place.
1) S.D of a set where the elements are all equal. A = {5.3,5.3,5.3} SD = 0
Note there is no exception to this. It can be integers and non-integers alike. The questions can be twisted from numbered balls with same number written on each one of them to students scoring same marks in an exam.
2) SD of a new set of numbers derived from old set, where a fixed number is added to each number in the old set to derive new set. Please note the wording - a fixed number or same number - No percentage is mentioned here.
A = {6, 2, 8, 7} SD = x, B = {9,5,11,10} SD = ? . You can see same number is added to each element. New SD will be same as old SD.
3) SD of a new set of numbers derived from old set, where a fixed percentage is added to each number in the old set to derive new set. Please note the wording - a fixed percentage is same as "same percentage"mentioned here.
A = {100, 200, 800, 700} SD = x, B = {110,220,880,770} SD = ? . You can see same percentage (=10%) is added to each element. New SD will be same as old SD + 10% increase of SD = 1.1x.
4) Countless question on SD of consecutive integers / numbers in Arithmetic Progression series
a) SD of consecutive integers/ AP series is exactly same regardless of starting point as long as number of elements in a set is same.
For example : A = (10, 15, 20) B = (95,100,105) C = (65,70,75) - All same SD [Please note it is important to be from same series or difference between elements is same when one set is compared to other]
b) SD of consecutive integers can be determined if # or No of elements in a series is given. That's all.
c) SD of AP series can be determined if difference between elements and # of elements are given. That's all.
In any of the cases a) b) c), SD is independent of starting integer.
5) GMAT Club math book has one excellent section on the new SD of a new set when an element is added to existing set. There are four cases depending on distance of new element from mean a)greater than b) less than c) equal to existing mean or d) distance zero. New SD will be a)greater than b) less than c) equal to existing SD or d) lowest in that order. For details GMAT club mathbook is there for free download.
-South City