You found Set 2 has 0 SD, so thats comes last. Eliminate A,C,E

Between B and D; Notice numbers in set 1 are closer together and hence would have a smaller SD;

Order should be III,I,II D

I. 72, 73, 74, 75, 76
II. 74, 74, 74, 74, 74
III. 62, 74, 74, 74, 89

calculating the square of the numerator of the Standard deviation formula

(-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 = 10
0^2 + 0^2 + 0^2 + 0^2 + 0^2 = 0
(-12)^2 + No need > 144

So III > I > II option D

Dear Shankar,

what you are saying in right but if we notice in option III middle numbers are same.
So if we say the IIIrd set has higher SD so all the deviations from mean should be same isnt it.

Please correct my understanding

I am not sure I understand your question properly,

In set III, you have 5 elements of which 3 are equal (74) but the other two elements are quite far off from 74 (12 and 15 units away).
If you notice Set I, its 5 consecutive integers (each differ from the previous by 1)

Imagine plotting the points on a graph, SetI will have all its elements close together whereas SetIII would be scattered, the very definition of SD.
In this case, looking at the numbers we can say its SD would be more than the set with consecutive integers.

But if all the 3 sets had numbers close together, we would need the formula for SD (or) the way 'neelgandham' has posted. That is a foolproof way to do it, but if the numbers given are obvious such as this, I prefer to skip doing math and save time.

[email protected] wrote:Dear Shankar,

what you are saying in right but if we notice in option III middle numbers are same.
So if we say the IIIrd set has higher SD so all the deviations from mean should be same isnt it.

Please correct my understanding

ok,

i got it now.

"neelgandham " can you please write the formula and its detail which you have used.

[email protected] wrote:ok,

i got it now.

"neelgandham " can you please write the formula and its detail which you have used.

Hello Aksurana,

Please find below the attachment(Self explanatory)