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When testings a hypothesis, statistics can be used to calculate the chances or probability of getting a result
Managers use statistics to assess risks. When a project has a high probability of being unsuccessful, managers will avoid the project.
They certainly wouldn't admit to it so there is no way of getting proper statistics on this.
Lawyers use a lot of statistics and there are some equations to deal with the strength of a legal document.
The importance of probability and statistics can be found in many business aspects. For example, a loan officer at a bank is going to need to analyze statistical data to determine the feasibility of a loan on a house in a given area. Scientists use probability and statistical data when performing experiments. It is also used in astronomy to calculate where a given star will be at a given time based on past statistical data.
wikipedia lists some of them under "Notation in probability and statistics". However, various academic disciplines have their own publication standards also. For example, if you were publishing in the field of psychology then you might be obliged to use the APA abbreviations.
Differential statistics are statistics that use calculus. Normally statistics would use algebra but differential statistics uses calculus instead of algebra.
Civil engineering has a lot of uncertainty associated with it. To deal with those uncertainties, engineers use statistics and probability as a tool. Example: load prediction on a structure is estimated using statistics, strength of steel/concrete is generally a varying one and it has to estimated using statistics. Generally, design is done based on codes which make the statistical analysis a simple deterministic one.
Usually mu is the symbol for the mean of a probability distribution. It is sometimes used as the average of a dataset (also called the mean of the dataset), although I prefer to use "x bar".
A distribution table would be primarily used in the field of statistics and probability. Collecting and interpreting data is much easier when compiled in this format.
Statistics is a branch of mathematics.