What is Statistics?
Statistics is a branch of mathematics that deals with the collection, review, and analysis of data. It is known for drawing the conclusions of data with the use of quantified models. Statistical analysis is a process of collecting and evaluating data and summarizing it into mathematical form.
Statistics can be defined as the study of the collection, analysis, interpretation, presentation, and organization of data. In simple words, it is a mathematical tool that is used to collect and summarize data.
Uncertainty and fluctuation in different fields and parameters can be determined only through statistical analysis. These uncertainties are determined by the probability that plays a very important role in statistics.
What is Statistics?
In simple words statistics is the study and manipulation of given data. It deals with the analysis and computation of given numerical data. Let us take into consideration some more definitions of statistics given by different authors here:
The Merriam-Webster dictionary defines the term statistics as “The particular data or facts and conditions of a people within a state - especially the values that can be expressed in numbers or in any other tabular or classified way”.
According to Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts or values in any department of inquiry placed in specific relation to each other”.
Statistics Examples
Some real-life examples of statistics are given below:
To find the mean of the marks obtained by each student in a class of 40 students, the average value is the statistics of the marks obtained.
Suppose you need to find the number of employed citizens in a city. If the city has a population of 10 lakh people, we will take a sample of 1000 people. Based on this, we can prepare the data, which is the statistic.
Basics of Statistics
Statistics consist of the measure of central tendency and the measure of dispersion. These central tendencies are actually the mean, median, and mode and dispersions comprise variance and standard deviation.
Mean is defined as the average of all the given data. Median is the central value when the given data is arranged in order. The mode determines the most frequent observations in the given data.
Variation can be defined as the measure of spread out of the collection of data. Standard deviation is defined as the measure of the dispersion of data from the mean and the square of the standard deviation is also equal to the variance.
Mathematical Statistics
Mathematical statistics is the usage of Mathematics to Statistics. The most common application of Mathematical statistics is the collection and analysis of facts about a country: its economy, and, military, population, number of employed citizens, GDP growth, etc. Mathematical techniques like mathematical analysis, linear algebra, stochastic analysis, differential equation, and measure-theoretic probability theory are used for different analytics.
Since probability uses statistics, Mathematical Statistics is an application of Probability theory.
For analyzing the data, two methods are used:
Descriptive Statistics: It is used to synopsize (or summarize) the data and their properties.
Inferential Statistics: It is used to get a conclusion from the data.
In descriptive statistics, the data or collection of data is described in the form of a summary. And the inferential stats are used to explain the descriptive one. Both of these types are used on a large scale.
There is one more type of statistics, in which descriptive statistics are transitioned into inferential stats.
Scope of Statistics
Statistics can be used in many major fields such as psychology, geology, sociology, weather forecasting, probability, and much more. The main purpose of statistics is to learn by analysis of data, it focuses on applications, and hence, it is distinctively considered as a mathematical science.
Methods in Statistics
The statistical process involves collecting, summarizing, analyzing, and interpreting variable numerical data. Some methods of statistics are given below.
Data collection
Data summarization
Statistical analysis
What is Data in Statistics?
Data can be defined as a collection of facts, such as numbers, words, measurements, observations, quantities etc.
Types of Data
Qualitative data- it is a form of descriptive data.
Example- She can write fast, He is tall.
Quantitative data- it is in the form of numerical information.
Example- An elephant has four legs.
Types of quantitative data
Discrete data- it has a fixed value that can be counted
Continuous data- it has no fixed value but has a range that can be measured.
Collecting and Summarizing Data
Data:
A collection of observations, facts about an object is known as Data. Data can be in numbers or in statement/descriptive form.
For example,
The statement “How many legs does this table have?”. Here, the counted (or collected) value of legs is known as data.
Data Organization of the collected data is required in order to be processed. Information can be provided by processing the data.
Description of Data
There are various ways to describe the data:
Mode:
Mode is the value that occurs very often in the list. It can be said that there is no mode value if no number is repeated in the list.
Median:
Median is the middle value of the list. Median divides the list into two halves.
Mean:
A mean is an average of all the numbers in the list. It can be calculated by adding up all the numbers and then dividing the sum by the number of values in the list.
Range:
The range is the difference between the largest and the smallest numbers.
Types of Statistics
Being a broad term, there exist different models of statistics:
Mean
A mean is an average of two or more numerals. Mean can be computed using Mathematical mean or Geometric mean. The mathematical mean shows how well the commodity performs over the period whereas the geometric mean shows the result of the investment of the same commodity over the same period.
Regression Analysis
It is a statistical process that determines the relationship between variables. It is the process of understanding how the value of a dependent variable changes when any of the independent variables is changed. For example, the price of the property fluctuates due to the particular industry or sector.
Skewness
Skewness is the measure of the distortion from the standard distribution in a set of data. A curve is said to be skewed if it is shifted to the left or to the right. If the curve is extended towards the right side, it is known as the positive skewed and if the curve is extended towards the left side, it is known as the left-skewed.
Kurtosis
Kurtosis is the measure of the tailedness in the frequency distribution. Data set may have heavy-tails or light-tails.
Variance
Variance in statistics is the measure of the data span. It is used to compare the performances of stocks over a period of time.
Representation of Data in Statistics
There are various ways to represent data. For example- graphs, charts and tables. The general representation of statistical data is done with the help of:
Bar Graph
Pie Chart
Line Graph
Pictograph
Histogram
Frequency Distribution
Bar Graph:
It is the rectangular bar representation of data. The bars can be horizontal or vertical. The length of the bar is proportional to the value that it represents. It represents data in the form of rectangular bars having length according to the values that they represent.
There are three types of bar graphs:
Vertical Bar Graph
Horizontal Bar Graph
Double bar Graph
The Representations of Vertical and Horizontal Bar Graphs are as Shown Below:
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A double bar graph is used to represent the two sets of data in the same graph.
A Representation of a Double Bar Graph is Shown as Below:
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Pie Chart:
It is also known as the Circle Graph as it uses sectors of the circle to represent the data. This graph is represented in the form of a circle which is divided into a various number of sectors where each sector represents a portion of the whole division.
Representation of the Pie chart is as shown below:
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Line Graph:
A line graph is represented by the straight line which connects the data points. It is represented by a series of data points called markers. Usually, a line graph is used to represent the change of the data over the period of time.
A Representation of the Line Graph is as Shown Below:
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Pictograph:
It is the representation of the frequency of data using the symbols or pictures. A symbol can represent one or more numbers of data. It represents data with the help of pictures.
A Representation of the Pictograph is as Shown Below:
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Venn Diagrams:
It is the pictorial representation which contains a box along with circles. The box represents the Sample Space and the circles represent the events. There can be three types of Venn diagrams:
Two or more than two separate circles (When there is no common data)
Overlapping Circles (When some of the data is common)
Circle within a circle (When the outer circle is the superset of the inner circle)
The Representation of Each of the Venn Diagrams is as Shown Below:
(Image will be uploaded soon)
Histogram:
It consists of rectangles Whose area is proportional to the frequency of a variable and whose width is equal to the class intervals.
Frequency Distribution:
The frequency of a value is represented by “f”. In a frequency table, specific data and values are arranged in ascending order of the given magnitude with their corresponding available frequencies.
Applications of Statistics
Information around the world can be determined mathematically through Statistics. There are various fields in which statistics are used:
Mathematics: Statistical methods like dispersion and probability are used to get more exact information.
Business: Various statistical tools are used to make quick decisions regarding the quality of the product, preferences of the customers, the target of the market etc.
Economics: Economics is totally dependent on statistics because statistical methods are used to calculate the various aspects like employment, inflation of the country. Exports and imports can be analysed through statistics.
Medical: Using statistics, the effectiveness of any drug can be analysed. A drug can be prescribed only after analysing it through statistics.
Quality Testing: Statistics samples are used to test the quality of all the products a Company produces.
Astronomy: Statistical methods help scientists to measure the size, distance, etc. of the objects in the universe.
Banking: Banks have several accounts to deposit customers’ money. At the same time, Banks have loan accounts as well to lend the money to the customers in order to earn more profit from it. For this purpose, a statistical approach is used to compare deposits and the requesting loans.
Science: Statistical methods are used in all fields of science.
Weather Forecasting: Statistical concepts are used to compare the previous weather with the current weather so as to predict the upcoming weather.
There are various other fields in which statistics is used. Statistics have a number of applications in various fields in Mathematics as well as in real life. Some of the major uses of statistics are given below:
Applied statistics, theoretical statistics, and mathematical statistics
Machine learning and data mining
Statistical computing
Statistics is effectively applied to the mathematics of the arts and sciences
Used for environmental and geographical studies
Used in the prediction of weather
