Youtor
Maths vs Probability Why does nature always follow Gaussian Distribution Bell Curve
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=ys0UToqn4CA
Almost everything we can observe and measure follows what’s known as a normal distribution, or a Bell curve. There’s a profound reason why. Whenever a baby is born, doctors measure a number of vital statistics about them: height, weight, number of fingers-and-toes, etc. A newborn child is generally considered healthy if they fall somewhere near the average in all of those categories, with a normal, healthy height and weight, and with 10 fingers-and-toes apiece. Sometimes, a child will have an unusually low or high height or weight, or greater or fewer than 10 fingers-and-toes, and the doctors will want to monitor them, ensuring that “not normal” doesn’t imply a problem. However, it turns out that there being an idea of “normal,” where “normal” means the most common set of outcomes, is universal to practically anything we dare to measure in large quantities. • The starting point, in anything that’s going to follow some sort of distribution, is what’s known as a random variable. It could be: • whether a coin lands heads or tails, • whether a rolled die lands on a 1, 2, 3, 4, 5, or 6, • what your measurement error is when you measure someone’s height, • what direction a spinner lands in when you spin it, • or many other examples. It simply refers to any case where there are multiple possible outcomes (rather than one and only one outcome) but that, when you make the measurement, you always and only get one particular answer. • It doesn’t matter what the likelihood of getting each outcome is. It doesn’t matter whether you have a fair coin or a biased coin. It doesn’t matter whether or not the die is weighted or unweighted, so long as there remains a non-zero chance of getting anything other than one option 100% of the time. And it doesn’t matter whether you have a discrete set of outcomes (e.g., a single die can only land on 1, 2, 3, 4, 5, or 6) or a continuous set of outcomes (a spinner can land on any angle from 0° to 360°, inclusive). Take enough measurements, and your sample will always follow a normal, or Bell curve, distribution. • In fact, every single Bell curve (or normal distribution) that exists can be shown, mathematically, to simply be a rescaled version of the standard normal distribution. The only rescalings that ever need to occur are: • a rescaling of the average value of the domain (x-axis, or the thing you’re measuring) so that the central value winds up representing the mean value (µ) of your outcomes, • a rescaling of the range of the domain (x-axis, which is again the thing you’re measuring) to reflect the standard deviation (σ) of your distribution, • and, finally, a rescaling of the probability density (y-axis, or the frequency of how likely you are to arrive at this particular outcome) so that the total area under the Bell curve equals 1, signifying a 100% probability that one of the outcomes represented by your probability graph will occur. • To know more check out the full video. • Thanks for watching.. • Social accounts link • Instagram- / scienceandmyths • Facebook Page- / scienceandmyths • Maths vs Probability | Why does nature always follow Gaussian Distribution / Bell Curve • FAIR-USE COPYRIGHT DISCLAIMER • This video is meant for Educational/Inspirational purpose only. We do not own any copyrights, all the rights go to their respective owners. The sole purpose of this video is to inspire, empower and educate the viewers.
#############################
