Thread by @kareem_carr

Statistics Formulas Explained!

This is a thread for data science beginners with a fun little twist at the end for the pros!

It will explain the formulas for:
1. the mean
2. the variance
3. and a fun link between both 🧵

Keep reading to find out more! 👇

Let's get warmed up by reviewing the definition of the mean or average of our data.

The variance formula looks a lot like taking an average but it's the average of the distance from the mean squared.

Variance is a mix of two ideas. The first idea is distance according to the Pythagorean formula. The second is the average. The formula for the variance combines these two ideas to make a kind of average distance. We write variance as σ² which is an analogy to c² from Pythagoras.

The fact that we're using the squared distance is important because once we pick the measure of distance, the variance and the mean become linked in a very natural way. I'll explain in the next tweet.

Notice how the minimum of F(y) links both the mean and the variance in a way that makes them stand out as special numbers.

What happens if we change the measure of distance to the absolute value instead of the square? Well, in this case the minimum value happens at the median.

Our choice of distance seems to link our measure of spread of our data to our measure of centrality (e.g. median, mean). It's interesting to ponder if this can be taken further. It can!

You can generalize these ideas to include the formula that the very popular K-means algorithm is minimizing. In that case, you may have already guessed but the "K-means" are "means" because they minimize that variance-like formula...but that's a story for another thread!

This kind of long-form content takes extra work so if you like it and want to show support, like and retweet the thread, and give me a follow! 🙂