DataScience Classroom Notes 02/Nov/2021

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
  • 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 Preview Preview
  • 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 Preview Preview
    • 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 Preview Preview Preview Preview
  • 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) Preview
  • 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) Preview

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