## Insight Things

### A scientific blog revealing the hidden links which shape our world

#### Tag: proof

Those of you who already have tested for the variance of data from a normal distribution may have asked themselves how the link between normal variance and chi-squared distribution arises. Trust me: The story, which I will tell you, is an exciting one! more →

One of statistic’s foundations lies in the fact you can add variances. Maybe you wonder a little bit, because the formula for the variance does not look like that at first glance. This article will show you the proof why and under which circumstances adding variances is a valid practice. Please check the information given in my articles on addition and multiplication of expected values, if you do not have collected experiences with it yet. more →

I’ve already explained in a demonstrative way how the formula for sum squared numbers arises. Not only will I only show in this article how to calculate simple series like 1+2+3+4+…., but you will also see how we enhance our findings to tackle more complicated series like 1³+2³+3³+…. These formulas are applied in many different contexts. more →

Have you ever wondered how the formula for the sum of squares (1+4+9+16+25+…) arises? Then this article is for you! We will see that there is a geometric interpretation for the problem of adding squared numbers. This interpretation will lead to the well-known formula (see “Sum of Squares, Cubes and Higher Powers” for higher powers). Curious? Then don’t let us waste time but start! more →

Maybe you had to multiply means or expected values already. If you know, for instance, how often people go shopping on average and how much money they spent on their shopping tours on average then you could multiply both to obtain the average amount spent. In this post I will explain why multiplying means and expected values is a valid operation. more →

In applied statistics you often have to combine data from different samples or distributions. One of the most frequently used operation here is to add means and expected values. For instance, you could sample people’s leg length, body and head height. The result when adding these means? It is the average body height, I hope! more →