Mathematical statistics is the application of math and its operations to statistics. Statistics was originally envisaged as the science of the state – the culmination and monitoring of information. Mathematical approaches utilized in various analytics include arithmetic analysis, linear algebra, differential equations, and measure-theoretic probability theory for defining and formulating statistics. The measures of central tendency and the measures of dispersion are the two fundamental statistical concepts.
The mean is the average obtained on addition of the total number of observations. When observations are organized in a certain order, the median is the central value. The modal value identifies the most frequently occurring observations in data collection. Variation is a measure of the dispersion of data in a collection. The standard deviation is a measure of the dispersion of data from the mean. The variance is defined as (standard deviation)2.
Data is an organized or unorganized cumulation of facts that can include integers, results, observations, readings, etc. Data can be exhibited into the following two types: 1. Qualitative data- As the name suggests, this data describes the quality. It is a descriptive analysis of the data given. For example- Rahul is a strong boy, the flower is yellow. 2. Quantitative data- This data depicts the quantity or the numerical information of the observations. For instance- The book has 400 pages, there are 28 states in India. The quantitative data can further be divided into discrete data and continuous data.
Data can be represented using graphs and pictures. The different methods of graph representation are:
A Bar Graph represents organized data using rectangular bars. The lengths of the bars are dependent on the values they represent. The rectangles in a bar graph can be oriented horizontally or vertically.
A Bar Graph represents organized data using rectangular bars. The lengths of the bars are dependent on the values they represent. The rectangles in a bar graph can be oriented horizontally or vertically.
A graph in which a circle has been split into Sectors. Each of these sectors account for a percentage of the total.
A line chart is composed of a sequence of data points linked by a straight line. The series of data points is referred to as a 'marker.'
Pictograph consists of a visual sign or a picture for a word or phrase, i.e., displaying data via images. For example, we can assign various numerical values to pictures of ice cream, cake, apple, pie, and banana to represent data.
A histogram is similar to a bar graph but with rectangles as graph representation. However, the size of the rectangle is proportional to a variable's frequency and whose breadth is equal to the class interval.
The frequency of a data value is frequently represented by the letter "f." A frequency table is created by grouping the gathered data values with their associated frequencies in ascending order of magnitude.