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22b. The concept of dispersion and the most “popular” statistics to quantify it.
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Dispersion in statistics is a way of describing how spread out a...
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21(a). Show how the general formula Mr encompasses various types of common averages and including (as limit) the geometric average (have a look at the proof)
If p is a non-zero real number, and x1 , … , xn are positive real numbers, then the generalized mean or power mean with exponent p of these positive real numbers is: For p = 0 we set it equal to the geometric mean (which is the limit of...
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21. Streaming algorithm for the mean () and the variance (2) (Knuth, Welford). Show with an example why the running mean formula is preferable to the definition formula.
in the previous post, we saw what mean is and now we will introduce a new term variance or standard deviation. The standard deviation is a measure of how much a dataset differs from its mean; it tells us how dispersed the data are. A dataset that’s pretty much clumped...
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20. Review the probability axioms, the union bound, the definition of probability and the Bayes Theorem
In this post, I will give an overview of the concepts which were already covered in the previous blog posts. First of all, let’s begin with the probability axioms, also known as Kolmogorov axioms. There are three of them and they are: 1. The probability of an event is a...
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19. The Markov inequality (about the arithmetic mean).
The Markov’s Inequality states that for a value a>0, we have for any random variable X that takes no negative values, the following upper bound is always observed: - Pr(X≥a) ≤ E(X)/a Markov’s inequality says that for a positive random variable X and any positive real number a, the probability...
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18. Find out about the various types of averages and find several real-world examples where they “naturally” occur
Data is a representation of real life. It’s an abstraction, and it’s impossible to encapsulate everything in a spreadsheet, which leads to uncertainty in the numbers. How well does a sample represent a full population? How likely is it that a dataset represents the truth? How much do you trust...
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17. How to define and use a bitmap and graphics object and animated display of image in a picture box using a timer.
Define The Bitmap b = New BitMap(width, height) The bitmap object constructor takes two inputs: the width and the height of the bitmap. If we are using a PictureBox, the input arguments can be the width and height of our PictureBox. Creation of the Graphics Object g = graphics.fromImage(b) Creation...
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16. Most useful conditional structures.
If…Then…Else Statement An If statement can be followed by an optional Else statement, which executes when the Boolean expression is false. Syntax The syntax of an If…Then… Else statement in VB.Net is as follows If(boolean_expression)Then ‘statement(s) will execute if the Boolean expression is true Else ‘statement(s) will execute if the...
