Statistics Part 2: Inferential Statistics

5 min readDec 24, 2022

Introduction:

The portion of mathematics that work on the accumulating, analyzing, predicting, and presenting the numerical data is known as Statistics.

Statistics is primarily categorized into two categories:

· Descriptive Statistics

· Inferential Statistics

In the previous blog I have written about descriptive statistics in this writing I will discuss about Inferential Statistics.

I will request to you all to read the first part before reading this, because I have discussed there sample & population and the concept of these will be required for inferential statistics.

Here is the link of the previous blog:

Statistics & Probability for Data Science First Part

Probability and Statistics are the base of Data Science. The probability theory is extremely helpful for making the…

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Now let us start from very scratch of Inferential Statistics.

What is Inferential Statistics?

Inferential statistics is an implemented method of statistics that makes conclusions (inferences) about the population data using the sample dataset.

E.g.: Average number of hours of Kinder Garden kids spend on watching cartoon in your state.

You can collect the data in two ways

1. By visiting every Kinder Garden school of your state. (Population)

2. By visiting every Kinder Garden school of your city. (Sample)

1st way is too much time taken and expensive in respect of 2nd way.

There also a possibility of the result of average number of hours of kinder garden kids spend on watching cartoon in your city is (a) extremely high or (b) extremely low, due to the facilities and life style of your city.

In inferential statistics I will discuss probability, probability distribution, hypothesis testing, t-test, chi-square test and ANOVA test in this blog.

Probability:

Definition of probability can be given as that the likeliness of happening or occurring an event.

As an example, we can take, if you want to draw a card from a standard deck of card then what is the percentage of being it a red card?

Here the solution is.

So,

Total number of cards n(S) = 52

Number of red card n(A) = 26

Hence, P(Red)=26/52 = ½ = 50%

So, the probability of being it the red card is 50%.

· Random Experiment:

A random experiment is a procedure through which experiment we see uncertain outcomes.

E.g., Rolling a dice

· Outcome:

Result of a Random Experiment.

E.g., If we roll a dice then outcome can be any one number of the dice {1,2,3,4,5,6}

· Sample Space:

Set of all probable result.

E.g., All the probable result of rolling a dice, à {1,2,3,4,5,6}

· Trials:

In a repeated Random Experiment, each Random Experiment is known as Trials.

· Event:

A subset of Sample Space.

E.g., Even & odd sets of the Random Experiment. Odd à {1,3,5} ; Even à {2,4,6}

· Random Variable:

Random Variable is numerical description of the Sample Space.

Probability Distributions:

Probability distribution is a list of all possible outcomes with their corresponding probability values of a Random Variable.

E.g.,

Types of Probability Distribution:

· Uniform Distribution

· Bernoulli Distribution

· Binomial Distribution

· Poisson Distribution

· Normal Distribution

Confidence Interval:

The range of values that is likely to include a population value with a certain degree of confidence is called Confidence interval. It is expressed in “%”.

E.g., 90% confidence interval for the population mean height of females (130 cm -150 cm) indicates that it is 90% confident that the mean height of female lies between 13 cm to 150 cm.

Hypothesis Testing:

Hypothesis testing is an act in statistics where researchers assume a result and propose it for the sake of argument so, that it can be verified to observe if that is true or not.