Mathematical Statistics and Its Importance

Statistics is the science of use and of categorization of data in order to draw inferences. The basic materials with which a statistician operates are numbers. Such numbers are usually called discrete data. Such data are usually called continuous, even though the measurements themselves can only be taken to a certain degree of fineness.

Normal distribution via Wikipedia

There are two principal ways to accumulate data: by sample or by census. There are several kinds of sampling. One of the most frequently employed methods is random sampling. In random sampling the probability that an element appears in the sample is unaffected by the appearance of another element, and each element of the population has an equal chance of appearing in the sample.

Histogram via Wikipedia

In stratified sampling, the population is separated into levels or strata, usually on the basis of some variable other than that being measured. Often stratified sampling is used to improve comparisons of groups within the population or to get more accuracy than that supplied by random sampling.

A discrete probability distribution via Wikipedia

In mathematical statistics it is often necessary to deal with hypothetical distribution functions. If we have an integrable function defined on the real axis, we may use it as a probability model. It is often convenient to think of samples and populations as forming distributions. In the case of measurement data, the variety is broken up into convenient-sized intervals, usually of equal length, and the frequency distribution gives the number of cases included in each interval.

Poisson Distribution via Wikipedia

An important continuous distribution function is the normal, or Gaussian, distribution. It is often used to approximate distributions of measurements in education, anthropology, industry, and psychology. Gaussian distribution has been found to be extremely useful as an approximation to many physical phenomena.

Binomial distribution via Wikipedia

The binomial distribution is an example of a discrete distribution. The binomial distribution is useful in dealing with public opinion polling, inspection of manufactured products, genetic problems, and games of chance.

The Poisson distribution is another useful discrete distribution. The Poisson distribution is useful in dealing with events which happen in fixed intervals of time or fixed areas, such as the number of counts on a Geiger counter in a 15-second interval, for example the number of accidents in a definite period of time.