A Painfree Walk through Standard Deviation

Imagine that there are two friends.

Tree and Tan.

Tan keeps complaining to Tree about how boring her quarantined life is.

One night, Tree tells her that he has got it hard as well.

Tan disagrees, saying that her friends live far off. "What are you talking about?", says Tree, "My friends live as far away from me as yours do."With a wrinkled brow, Tan tells him that the mean distance between their house and that of their friends are the same. Tree lets out a huuuuge sigh and informs her of a metric called Standard Deviation.

What exactly is Standard Deviation?

According to Wikipedia, it is a quantity expressing by how much the members of a group differ from the mean value of the group.

To understand this better, we need to delve into the example of Tree and Tan again.

These two dickheads, decide to write down the distance between their houses and their friends' on a piece of paper.

Tan:-

1. Chandu: 200 km

2. Bhanno :500km

3.Anirban:0.8km

4.Sug:8 km

Mean distance =177.2km

Tree:-

1.Tanisha:177km

2.Debraj:175km

3.Shush: 177.4km

4.Apratim: 179.4km

Mean distance=177.2km, again.

So, the average distance comes out to be the same for both the cases, Insistent on being childish, they decide to calculate how spread out their friends' houses are from theirs .This is where they need standard deviation.

The general formula for S.D, is calculated as,

SD= Square root of (E/N)

E= Summation of squares of D1, D2...DN

N= Number of data points( Friends, in this situation.)

DK= Difference of the value of kth point from the mean.

Using this formula, the standard deviation for Tan comes out to be 202.77km while that for Tree is 1.56 km. Needless to sat, that Tan's friends are spread out over the country in a wider manner as compared to those of Tree. This should hardly matter, though as they are currently all quanrantined and communicating virtually :) .