Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data.
According to MerriamWebster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.
According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.
Mathematical Statistics
Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state — the collection and analysis of facts about a country: its economy, and, military, population, and so forth.
Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis,differential equation and measuretheoretic probability theory.
Scope
Statistics is used in many sectors such as psychology, geology, sociology, weather forecasting, probability and much more. The goal of statistics is to gain understanding from data it focuses on applications and hence, it is distinctively considered as a Mathematical science.
Methods
The methods of collecting, summarizing, analyzing, and interpreting variable numerical data. Here are some of the methods provided below.
 Data collection
 Data summarization
 Statistical analysis
Data
Data is a collection of facts, such as numbers, words, measurements, observations etc.
Types of Data
 Qualitative data it is descriptive data.
Example She can run fast, He is thin.
 Quantitative data it is numerical information.
Example An Octopus is an Eight legged creature.
Types of quantitative data
 Discrete data has a particular fixed value.It can be counted
 Continuous data is not fixed but has a range of data.It can be measured.
Representation of Data
A Bar Graph represent grouped data with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. 

A type of graph in which a circle is divided into Sectors that each represent a proportion of the whole. 

The line chart is represented by a series of datapoints connected with a straight line 

A pictorial symbol for a word or phrase, i.e. showing data with the help of pictures. Such as Apple, Banana & Cherry can have different number, it is just a representation of data. 

Histogram
A diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval. 

Frequency Distribution The frequency of a data value is often represented by “f.” A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies. 
Formulas used
Sample Mean (\(\bar{x}\))  \(\frac{\sum x}{n}\) 
Population Mean (\(\mu\))  \(\frac{\sum x}{N}\) 
Sample Standard Deviation (s)  \(\sqrt{\frac{\sum (x\bar{x})^{2} }{n1}}\) 
Population Standard Deviation (\(\sigma\))  \(\sigma = \sqrt{\frac{(x\mu )^{2}}{N}}\) 
Sample Variance (\(s^{2}\))  \(s^{2} = \frac{\sum (x_{i}\bar{x})}{n1}\) 
Population Variance (\(\sigma ^{2}\))  \(\sigma ^{2} = \frac{\sum (x_{i} – \bar{x})}{N}\)< 
Range (R)  Largest data value – smallest data value 
Application
 Some of the application of statistic are given below:
 Applied statistics, theoretical statistics and mathematical statistics
 Machine learning and data mining
 Statistics in society
 Statistical computing
 Statistics applied to mathematics or the arts
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