adkikani wrote:
niks18Can you explain why are we focusing on patterns by difference between two adjacent no?
As per my understanding the SD should be approx difference of each no from mean.
Also note that adding / subtracting same integer will not change SD, but here we are adding
different numbers to the list. How can this be a conclusive factor to determine same SD?
Hi
adkikaniAt first I would suggest that you keep the property in mind as explained by
mikemcgarry in his earlier post. it will save you from unnecessary calculation.
As you rightly mentioned that adding / subtracting same integer will not change SD. There is another property which says if you multiply each element of the set by \(k\), then you multiply the standard deviation by \(|k|\) (remember SD is always positive because it is square root of variance. Variance is the average of the squares of difference between each element and mean, so variance will always be positive)
Set Q {5, 8, 13, 21, 34}. let's assume it's SD is \(d\)
Set I, I hope is clear to you as you have used the addition property.
Set III {46, 59, 67, 72, 75}
Now add \(-80\) to each element of the set, you will get {-34,-21,-13,-8,-5}. Re-arrange (if may like to do so to see a pattern, otherwise not required) {-5,-8,-13,-21,-34}
This is same as set Q multiplied by \(-1\), so SD of this set will be \(d*|-1|=d=\)
same as set Qso we can also derive that if basic pattern of spacing between adjacent element of two sets are same then SD will be equal.
This question tests basically few properties of SD which you can easily deduce if you know the STEP TO CALCULATE SD of a given set