## Inferential Statistics

- Descriptive Statistics describes data, where as inferential statistics allows us to make predictions (inferences) from that data.
- With inferential statistics we take data from samples and make generalizations about population.
- For example:
- We might stand in a mall and ask a sample of 100 people if they like shopping at ‘Shoppers Stop’.
- With Descriptive Statistics
- We could make a bar chart/pie chart with yes or no aswers

- With inferential statistics
- We could use our research to reason that around 65-70% of the population would like shopping at
`shoppers stop`

- We could use our research to reason that around 65-70% of the population would like shopping at

- Distribution is one of the most important concept to understand in inferential statistics.

## Distributions

- When we speak about distributions, we mean probability distributions
- Definitions:
- A distribution is a function that shows the possible values for a variable and how often they occur.
- In Probability theory and statistics, a probability distribution is a mathematical function that stated, in simple terms can be thought of as providing the probabilities of occurance of different possible outcomes in an experiment
- Examples:
- Normal Distribution
- Students t-distribution
- Poisson Distribution
- Uniform Distribution
- Binomial Distribution
- Exponential Distribution

- Example: Lets try to understand the distribution by considering a scenario of rolling one dice
- Activity: Lets try to understand the distribution by considering a scenario of rolling two die’s and we need a distribution of sum of two dies
- Refer Here for the xlsx containing dice problems solution

## Normal Distribution

- The normal distribution is also known as Gaussian distribution or the Bell Curve.
- This is one of the most common distribution due to following reasons:
- It approximates wide variety of random variables
- Distribution of sample means with large enought sample sizes could be approximated to normal
- All computable statistics are elegant
- Heavily used in regression analysis
- Good track record

- Examples:
- Biology
- IQ tests
- Stock market information

- This distribution is represented as
- Keeping the standard deviation constant, the graph of a normal distribution with
- smaller mean would look the same way, but be situated to the left (brown)
- larger mean would look the same way, but be situated to the right (red)

- Keeping the mean constant, a normal distribution with
- smaller deviation would be situated in same spot but have a higher peak and thinner tails (red)
- a larger standard deviation would be situated in the same spot but have lower peak & fatter tails (in brown)