Statistics and its types

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What is Statistics?

Statistics is the branch of science in which we deal with the collection, analysis, and interpretation of numeric data related to any field. In reality, it is a type of quantitative equation that uses various quantitative models to generate a set of experimental results or investigations of real-world phenomena. Data collection, analysis, interpretation, and presentation are all issues that are addressed in this field of applied mathematics. Statistics focuses on the use of statistics for solving challenging issues. Some individuals believe statistics to be a separate mathematical science as opposed to a subfield of math. Statistics simplify your work and give you a clear, concise image of the tasks you accomplish on a routine basis.


The terminology used in statistics:

Population:

It is actually a group of a set of people, things, or events whose characteristics need to be examined.

Sample:

It is a population subgroup.

Types of Statistics:

        1)  Descriptive Statistics

       2) Inferential Statistics                                                         

What is Descriptive Statistics?

 Descriptive statistics make use of information to describe the community using a chart, graph, or numerical computation. It offers a summary of data in graph format. It serves only to summarize many objects, etc. This can be separated into the two groups listed below:

Types of Descriptive Statistics



  1.    A measure of central tendency    

                      A data set or sample set's Centre or a specific value is represented by the measure of central tendency, which is also referred to as summary statistics. There are three widely used measures of central tendency in statistics, as illustrated below:    

  • Mean:        

                    It is an indicator of the average across all values in a sample collection.

Example 

Items

X

Fruits

12   

Dry fruits

15       

Vegetables

20

 




        Mean= Sum of all items ÷ Total no of items

        Mean= 12+15+20 ÷ 3     

        Mean= 47 ÷ 3 = 33.66  

  • Median:

  It is a measurement of a sample set's median value. These first identify the precise middle of the data set after it is sorted from the lowest to the highest value.   

Example      

Items

     X

Fruits

     17

Dry fruits

      15

Vegetable

       10

Snacks

       20
             







Ordering the set from Lowest to Highest = 10    15    17   20

    Median = 15+17 ÷ 2         

    Median = 16

  • Mode         


 The sample set's most frequent value is this one. Mode is the value that appears the most frequently in the core set.    

Example 


      2  5   6  6   3  1   6   4   5   5   9   2

    Mode = 6

  • Geometric mean

The Geometric Mean (GM) in mathematics is the average value or mean that represents the central tendency of a group of integers by calculating the multiplication of their values.
In the other language, the geometric mean is the product of n integers divided by the nth root.

  • Formula

  1. Geometric mean = √x₁ · x₂ · ... · xₙ
  2. Geometric Mean = (x₁ · x₂ · ... · xₙ)1/n          

  • Harmonic mean  
A particular kind of numerical average is the harmonic mean. It is determined by multiplying the total number of data by each number in the series reciprocal. The mean of the corresponding sides is therefore the reciprocal of the harmonic mean.

  • Formula
HM = n / [(1/x1)+(1/x2)+(1/x3)+…+(1/xn)]

2.  The measure of Variability:


A summary statistic that depicts the degree of dispersion in a dataset is known as a measure of variability. A sample or population's variability is described using the measure of variability, also referred to as the measure of dispersion. How widely separated are the values? Measures of variability describe how much the data points typically deviate from the center, whereas a central tendency measurement describes the typical value. In the scope of a range of values, we discuss variability. A low dispersion means the data tend to be firmly grouped around the center. High dispersion indicates that they are likely to scatter farther. There are three widely used measures of variability in statistics, as illustrated below:

  • Range


It is a measurement of how values in a sample group or data set should be spaced apart.

  • Formula


                             Range= Maximum value - Minimum value
 

  • Variance



Variability is measured by the variance. The average of the square deviations from the mean is used to calculate it.
The degree of dispersion in your set of data is indicated by variance. The variance is greater with respect to the mean the more dispersed the data.

  • Variance is an estimate of the range of values within a set of data.
  • It specifically analyses how widely distributed the data are from the sample mean.
  • Marketers use variance to assess an investment's risk level and potential profitability.
  • To determine the appropriate asset allocation, variation is also used in finance to analyze the relative strength of each asset in a portfolio.

Formula


                      S2= ∑ni=1 [(xi - ͞x)2 ÷ n]  

In this formula, n stands for the overall number of data points, x for the average number of data points, and xi for individual points of data.

  • Dispersion:


It measures how widely apart a batch of data is from the mean. The statistical concept of dispersion, which can be quantified by a number of different statistics including range, variance, and standard deviation, refers to the magnitude of the distribution of values anticipated for a given variable.

  • Formula


             σ= √ (1÷n) ∑ni=1 (xi - μ)2 



2. Inferential Statistics


Utilizing a sample of data drawn from the population, inferential statistics draws conclusions and makes predictions about the population. To get a conclusion, it applies probabilities to huge data and generalizes the results. It serves just to clarify the meaning of descriptive statistics. It serves just as a tool for analysis, result interpretation, and conclusion-making. The primary goal of hypothesis testing, which is to reject the null hypothesis, is what inferential statistics are mostly linked to and associated with.

A sort of inferential process known as hypothesis testing uses sample data to analyze and gauge the veracity of a population-based hypothesis. Typically, inferential statistics are used to assess the strength of relationships within samples. But getting population data and selecting a random sample is exceedingly challenging.


The following steps can be used to perform inferential statistics:

  1. Obtain a theory, then use it.
  2. Make a hypothesis for your research.
  3. Use variables or operationalize
  4. Determine or figure out the population that we can use in learning materials.
  5. Create a null hypothesis or make one up for this demographic.
  6. Simply conduct the study by gathering a sample of kids from the general population.
  7. Then, run all statistical tests to determine whether the sample's features are enough different from those predicted by the null hypothesis for us to be able to identify and reject the null hypothesis.
  Types of Inferential Statistics   

    Inferential statistics of all kinds are used often today and are simple to understand. Here are some of them: 

  1.   One sample difference test/one sample test of the hypothesis
  2. Tables of Confidence Intervals and Chi-Square Statistics
  3. ANOVA or T-test
  4. Correlation by Pearson
  5. Regression using Bi-variate
  6. Several Variable Regression              

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