# Statistics Formula: Where did it come from?

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In summary, the conversation discusses the formula used to calculate variance in statistics, specifically in relation to the mean and standard deviation. The formula takes into account the number of data points and uses (n-1) to adjust for the fact that the mean is calculated from the same data set. This formula can be found on various sources, including the Wikipedia page on variance.

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This may not answer your question completely. However the mathematical expectation (theoretical average) of s2 is the theoretical variance of the statistical average.

This will not be completely answer it but
In statistics the idea is to get a picture of how lots of numbers act by using a few numbers. The first statistic often used is the mean
mean=sum/number
If our data has mean 0 we might like to know are all the numbers zero, most, maybe half are 1000000000 and half -1000000000. We want an idea of spreadoutness. so we consider
mean(x-mean(x))
but it is zero we cure that with
mean((x-mean(x))^2)
but we are using n numbers like n+1 (mean(x) depends on x hence is not its own number)
so we do
(n/(n-1))mean((x-mean(x))^2)
but it is squarey so
sqrt((n/(n-1))mean((x-mean(x))^2))
which is the standard deviation we know and love

That helps thx. I now get most of the formula except why is it (n-1)?

## 1. Where did statistics formula originate from?

The origins of statistics can be traced back to ancient civilizations such as the Babylonians, Egyptians, and Greeks who used rudimentary forms of data collection and analysis for various purposes. However, modern statistics as we know it today was developed in the 17th century by mathematicians such as Blaise Pascal and Pierre de Fermat, and later expanded upon by Sir Francis Galton and Sir Ronald Fisher.

## 2. How are statistics formulas derived?

Statistics formulas are derived from mathematical principles and techniques such as probability theory, calculus, and linear algebra. These formulas are used to summarize and analyze data, make predictions, and test hypotheses.

## 3. Why are there different statistics formulas?

There are different statistics formulas because they are used for different purposes and scenarios. For example, there are formulas for descriptive statistics, which summarize and describe data, and formulas for inferential statistics, which make inferences and predictions about a larger population based on a sample of data.

## 4. How are statistics formulas used in scientific research?

Statistics formulas are an essential tool in scientific research as they allow researchers to analyze and interpret data, make informed conclusions, and test hypotheses. They are used in various fields such as psychology, biology, economics, and many others to draw meaningful insights from data.

## 5. Are statistics formulas always accurate?

Statistics formulas are based on mathematical principles and are generally considered to be reliable. However, they are subject to limitations and assumptions, and their accuracy depends on the quality and representativeness of the data being analyzed. It is important for researchers to be aware of these limitations and use statistics formulas appropriately.