Also called

*Gaussian*distribution. OK, many things in this world tends, and should do, to be normally distributed.
Any distribution is a representation of how the information or data is distributed. We mainly look for its central tendency (

*mean*) and variability (*variance*). That's why the normal distribution is usually written as:*N ~ (Mu, Sigma^2)*

For example: the weight of most adult (who still youth) people will normally be centered around some values. Yes, you right there is a diversity: some are slim and some are obese.

We may expect the average weight for people (example: ages 20 to 30) to be between 70 to 74 kg. OK, let's consider it as 72 (this is the mean value).

Let

*x*represents the weight of a random person. Thus,*Expected Value [x] = mean [x] = Mu = 72 kg*

If we have a sample, we can compute the variance (sigma^2) to indicate variability. But we may here think as following:

*Variance = Sigma^2 = Expected Value [(x-Mu)^2]*

*Standard Deviation = Sigma = square root [variance]*

Got it? The variance is just the

*squared*expected (average) difference between values of*x*and its mean*Mu*.
Assume that the weights could vary (in

*average*) +4 or -4 kgs from the mean value. Thus, we have*Sigma approx= 4*

*Variance approx= 16*

We may conclude, the probability distribution of youth people weight:

*weight = x ~ N (72, 16)*

Note: this is just an illustrative example where real information may be different depending on location or other factors.

Facts for any normally distributed data:

- Within
*1 sigma*distance/difference from the mean value (to left and right), there exist about 68% of data. - Within
*2 sigmas*distance/difference from the mean value (to left and right), there exist about 95% of data.

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