Introduction to Statistics and Its types

Statistics is a field of mathematics that deals with the collection, organizing, and interpretation of numerical data. It is used to visualize, analyze, and draw the conclusion from data.

Some frequently used terms in statistics:

Population: Total dataset related to some particular use case. Example Want to know how many people are below the poverty line in the country.

Sample: Sample is a subset of the population. Example Now as we want to know how many people are below the poverty line in our country. But considering the whole population of this survey is next to impossible. So we select as a chunk of population for performing survey and based on that we find conclusion about how many people are below the poverty line in our country.

Variable: Type of every element in population or sample.

Experiment: Collecting data and analyzing it with a different hypothesis.

Parameter: Various parameters are used in statistics such as mean, median, mode, standard deviation, etc.

Types of statistics:

  1. Descriptive Statistics
  2. Inferential Statistics

Descriptive Statistics: Descriptive statistics deals with numerical data. It summarizes data based on the number, graph, and calculations. It describes data based on mean, median, mode, standard deviation.

Example: We have marks of a student ‘s1’ in English and math, suppose in English s1 scores 84 marks and in math, he scores 90 marks. Now I will ask you a question in which subject s1 performs better so you will say in math. But now if I give average marks of all students in class in English average marks is 83 and in math, the average is 94, So we can easily say s1 performs better in English wrt class.

Here descriptive statistics help us in analyzing result.

Mode of central tendency:

Mean: Mean is a average value of all values in dataset.

mean=Sum of terms/Number of terms

l=[10,20,30,40]

mean=(10+20+30+40)/4=100/4=25

Median: It measures central value of dataset. We arrange data in ascending order than find mid value.

https://www.media4math.com/library/formulas-median
https://www.media4math.com/library/formulas-median

Mode: Mode provides value that is most frequently occurring in our dataset.

l=[1,2,4,3,7,1,1,2,8,9]

mode=1

Range: Range is difference between highest and lowest value in data.

range=|highest value-lowest value|

l=[11,42,80,43,48,12]

range=80-11=69

Standard deviation: It is used to find how far our data is from the mean.

Inferential Statistics: Inferential statistics is a generalization, decision about the population based on a sample. Here sample that we select for making conclusions should be unbiased.

Inferential statistics is used to make inferences from data whereas descriptive statistics simply describes what’s going on in our data.