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I’d say statistics is the branch of mathematics that concerns itself with finding patterns or relationships from given data. It can also be used to determine how likely a certain outcome is given an initial set of probabilities.As for how it relates to math, it is math. Don’t know what else to say.Usually statistics is used in science to try to find correlations between two or more things or events. For example, to answer the question “Is man-made activity contributing to global warming?” we’d first get data for the average temperature of the Earth for the past 100,000 years or so. Then we’d check to see how much the temperature fluctuates on average. Then we’d see if we lie outside of that fluctuation, and if so then by how much. Depending on what the data is you can determine the probability of whether or not modern man is causing global warming.

Like all mathematics branches, statistics has anxioms. If you want to find them, you have to dig deep into probability theory and size theory ( [external link] ) though.Statistics has laws/theorems like any other mathematics branch than can be proved with the anxioms.So yes, it is a science and not something “made up” that happens to work, and may be applied to experiments to draw meaningfull conclusions.PS: An interesting thought for your essay:A big consequence of statistics is that ANY experiment (ever done by anonyone) always has a probablility % involved. For example if you do 10,000 experiments and they all end up the same way, statistics will say “it will always end up this way, with probability 99.9999%”. To be 100% sure, you have to do an infinite amount of experiments. So all of science is build out of 99.99999% certainties, that can come crashing down any moment. (Well not really crashing, it would still have a simplified view of reality. There’s many example’s, like how relativity replaced Newton’s model for gravitation.)

You will obviously need to do alot more work for an essay than use answers on here.But, of course Statistics is a branch of mathematics. Statistics uses numbers, charts, graphs, interpolation, and much much more. It should be fairly obvious how it relates to math.It can absoutely be applied to Science. Just think of doing a lab report. Many times you will retreive data while doing the lab and will have to use the data to produce something further. Many times you will be doing statistics whether you know it or not. A common example can be a best-fit line for your data that you may have graphed.