# Statistics Calculator

## How To Use Statistics Calculator

Statistics is the discipline that concerns the collection, organization, analysis, interpretation and presentation of data.

In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.

Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation

Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, or as a branch of mathematics.

Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty and decision making in the face of uncertainty.

In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics such as "all people living in a country"

Statistical calculation:

Let the set of n terms be x1, x2, x3, x4, x5, ......, xn.

Let the Maximum Value be x9 and the Minimum Value be x4.

Then the Range will be x9 - x4.

$$Sum = \sum_{i=1}^n x_i$$ $$Sum = x_1 + x_2 + x_3 + ... + x_n$$ $$Mean,\hspace{1cm}\mu = \frac{1}{n}\sum_{i=1}^n x_i$$ $$\mu = \frac{1}{n}(x_1 + x_2 + x_3 + ... + x_n)$$ In other words, $$\mu = \frac{Sum \hspace{0.2cm}of \hspace{0.2cm}terms}{Number\hspace{0.2cm} of\hspace{0.2cm} terms}$$

For finding the Median, first sort the data in the Ascending or Descending Order.Then

if the number of terms is odd, then the median will be ($$\frac{n\hspace{0.1cm}+\hspace{0.1cm}1}{2}$$) th term.

if the number of terms is even, then the median will be $$\frac{1}{2}$$($$\frac{n}{2}$$ th term + $$(\frac{n}{2}\hspace{0.1cm}+\hspace{0.1cm}1)$$ th term).

The term with Maximum Occurences will be Mode.

$$Variance,\hspace{0.1cm}\sigma^2 = \frac{1}{n}\sum_{i=1}^n (x_i\hspace{0.1cm}-\hspace{0.1cm}\mu)^2$$ $$Standard\hspace{0.1cm}Deviation,\hspace{0.1cm}\sigma = \sqrt{\sigma^2}$$ $$\sigma= \sqrt{\frac{1}{n}\sum_{i=1}^n (x_i\hspace{0.1cm}-\hspace{0.1cm}\mu)^2}$$

Statistical methods:

1. Descriptive statistics is a summary statistic that quantitatively describes or summarizes features of a collection of information.

2. Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution.

For statistical calculation using above statsistics calculator, you have to just write the comma separated values in the given input box and press the calculate button, you will get the result. 