In the name of Allah, most gracious and most merciful,
“Sigma” was staring at a bunch of numbers on the screen wondering how on earth will he make sense of them! While in this helpless state his friend “Mu” came next to him and said:
Mu: I understand your feelings. This seems overwhelming.
Sigma: Yes, I have been starring all night, and wonder how could I use these numbers. You know this data seems useless to me; I won’t try anymore.
Mu: Man, come on we are in 2022. You are not the first one to face this problem, people have faced similar problems years ago and have found solutions for them. I won’t tell you the solution, but I will give you an example of how science progresses so you can come to appreciate science more and look at the fundamentals you forgot during college to refresh your knowledge and live another new life! A life where you are driven by curiosity since you understand the proper tools to solve peoples’ problems.
Sigma’s face started to blossom with hope. Hope seems magical when it touches pessimistic people.
Mu: We humans can’t process this much data since our brain leans towards understanding the big picture, these 10,000 numbers are useless unless we make some sort of grouping or abstraction. Calm down man, forget about data. Now let us assume that you want to describe anything on earth, how will you do it?
Sigma: Maybe look at its size, shape, mass, volume, and width.
Mu: Yes exactly, it is very similar to that. But you are not grouping things in a logical way to simplify things. Size, volume, and width can all be reduced to just a distance, okay? Just keep this in mind. What about the shape?
Sigma: I don’t know, shapes are just shapes.
Mu: Yes, exactly my friend Sigma. Shapes are just shapes, so leave these now for a while. Deal?
Sigma: Deal! Now we have nothing left but mass.
Mu: Okay, but the mass is used for physical objects and not for making sense of numbers, so just forget about it. We could make an analogy for it, but leave it for now, to avoid confusing yourself.
Mu: Now we have shape and distance, don’t you see anything in common.
Sigma: No, I don’t know.
Mu: Man come on! Don’t you remember that I told you that you are describing something?
Sigma: Hmmm, so I think the shape is enough. But we could describe that shape by measurements of distances.
Mu: Exactly, Sigma. Mathematicians are humans like us, thinking logically so I now agree with you. Think a little bit more.
Sigma: We can describe shapes with maybe a length and width if it is a rectangle.
Mu: But I want a general thing even for a curvy shape. I will tell you. If I am talking about circles which has a very high curvature then I have a center, right?
Sigma: Yes, so we have the center now, and a distance.
Mu: If we have a center and a distance, what do we want this distance to describe for us? Distance is just spread, and that’s it.
Sigma’s face was not astonished and then said: Is that all you have?
Mu: Yes, after rearranging what we have reached, we just need to convert all these numbers that you see into some shape you can see, and this shape is described simply by its center, and by how spread it is. That is a concrete concept in Descriptive Statistics.
Sigma: Wonderful! What a different way of approaching things? I forgot that from college although I have studied it. This seems much more intuitive and logical to me. Thank you, my friend.
Descriptive statistics wants us to describe data by shapes or well-known distributions, and these shapes can basically be described by their center or Average or Mean “Mu”, and spread or standard deviation “Sigma”. Just keep in mind, a shape with center and spread.
Learning while appreciating how science has developed develops a critical thinking mentality that not only understands but produces. To produce you need to train yourself to produce, and understand how things are produced. Of course, this story is contrived and not a true one, but I hope it has been useful to you.
Thank you. I hope this post has been beneficial to you. I would appreciate any comments if anyone needed more clarifications or if anyone has seen something wrong in what I have written in order to modify it, and I would also appreciate any possible enhancements or suggestions. We are humans, and errors are expected from us, but we could also minimize those errors by learning from our mistakes and by seeking to improve what we do.
Allah bless our master Muhammad and his family.