Statistics


Statistics is a branch of mathematics which 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 the mathematical form. 

Mathematical Statistics

Since probability uses statistics, Mathematical Statistics is an application of Probability theory.

For analysing the data, two methods are used:

  1. Descriptive Statistics: It is used to synopsize (or summarize) the data and their properties.

  2. Inferential Statistics: It is used to get a conclusion from the data. 

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. 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 which 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 fluctuating 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 the 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.

Applications of Statistics

Information around the world can be determined mathematically through Statistics. There are various fields in which statistics are used:

  1. Mathematics: Statistical methods like dispersion and probability are used to get more exact information.

  2. 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. 

  3. 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.

  4. Medical: Using statistics, the effectiveness of any drug can be analysed. A drug can be prescribed only after analysing it through statistics.

  5. Quality Testing: Statistics samples are used to test the quality of all the products a Company produce.

  6. Astronomy: Statistical methods help the scientists to measure the size, distance etc. of the objects in the universe. 

  7. Banking: Banks have several accounts to deposit customer’s 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 between deposits and the requesting loans.

  8. Science: Statistical methods are used in all fields of science. 

  9. 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. 

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 this table has?”. 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 which 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 of the largest and the smallest numbers.

Representation of Data in Statistics

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. 

There are three types of bar graphs:

  1. Vertical Bar Graph

  2. Horizontal Bar Graph

  3. Double bar Graph

The Representations of Vertical and Horizontal Bar Graphs are as Shown Below:

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:

Pie Chart:

It is also known as the Circle Graph as it uses sectors of circle to represent the data. 

Representation of the Pie chart is as shown below:

Line Graph:

A line graph is represented by the straight line which connects the data points. 

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:

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. 

A Representation of the Pictograph is as Shown Below:

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:

  1. Two or more than two separate circles (When there is no common data)

  2. Overlapping Circles (When some of the data is common)

  3. 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: