What is Statistics?

Question

In Mathematics, what is Statistics? For myself I just want to know what Statistics mean in it's purest form? also I need a much simpler definition or explanation for kids aged 4-10. Need to explain probability to kids, so I have to explain Statistics first.

Answer 1

In the simplest context, a statistic (small 's') is a function whose input is a data set and whose output is some real number. We then define Statistics (big 'S') to be the study of these types of functions. (this is what one of the comments initially said)

Of course, we try to avoid any ounce of formality when introducing a topic, especially to children, so to them, I think a more appropriate definition (even if it's imprecise) would be:

"Statistics is the study of how to summarize large data sets and how meaningful those summaries are."

For instance, the mean, median, and mode provide numbers which summarize "where" the data generally is. Likewise, the variance or standard deviation provide numbers which summarize how close together the data generally is. We can even talk about much more complicated values that summarize a data set, but these are the ones that are most likely to be seen in the real world.

Answer 2

Mathematics is the abstract science of numbers, quantity and space. Mathematics may be studied in its own right (pure mathematics), or as it is applied to other disciplines such as physics and engineering (applied mathematics).

Statistics is the science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions as a whole from those in a representative sample. It can be considered as a branch of applied mathematics concerned with collecting, organizing, and interpreting data. The data are represented by means of graphs.

Mathematicians solve problems. Problems they work on range from pure mathematical problems to applied problems. Mathematicians try to find common features in seemingly distinct problems. That is, they look for patterns. They classify what behaviors can result from certain systems.

Statisticians develop techniques to overcome problems in data collection and analysis. They use statistical methods to collect and analyze data and to help solve real-world problems in business, engineering, healthcare and other fields.

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Ref.: https://scse.d.umn.edu/about/departments-and-programs/mathematics-statistics-department/what-math

Answer 3

To understand what statistics is, you need to contrast it with probability.

Probability deduces how likely events are based on certain assumptions. If I asked you how likely you were to get exactly two heads when tossing a coin five times, you'd probably assume each toss is independent, with a probability of $\frac12$ of giving heads.

Statistics is how we test such assumptions by looking at events that really happened. If all five tosses gave heads, that might not prove anything's amiss, since in theory it has a $1$ in $32$ chance. By "in theory", I mean on our assumptions, which in this context we call a null hypothesis. We might call the null hypothesis into question, however, if $70$ of $100$ tosses gave heads.