Normal Distribution - Explained Simply (part 1)

I describe the standard normal distribution and its properties with respect to the percentage of observations within each standard deviation. I also make reference to two key statistical demarcation points (i.e., 1.96 and 2.58) and their relationship to the normal distribution. Finally, I mention two tests that can be used to test normal distributions for statistical significance.

normal distribution, normal probability distribution, standard normal distribution, normal distribution curve, bell shaped curve

[boopbloo]

I see a lot of people are still confused on this video, so maybe my explanation will help.
68% of the population is within 1 standard deviation of the mean.
95% of the population is within 2 standard deviations of the mean.
99.7% of the population is within 3 standard deviations of the mean.
So, if I ask you what the 50th percentile is in a data set, then its the mew or mean(same thing), so its the very center(where the 0 is on the video).
if I ask you what the 40th percentile is it would fall within -1(SD) and the mean.
if I ask you what the 80th percentile is it would fall between the mean and +1(SD) away from the mean.
Hope this helps a little bit. Happy studying and glhf!!

[levitemusicstd]

Let me try to explain these percentages for the students that are struggling with it.

The good news, is this: It is NOT within your ability to calculate these percentages on your own and you will not be expected to. This is a problem that can only be solved through advanced integral calculus, and it is problem that only a small handful of calculus enthusiasts have the ability to solve. BUT, you better be damn clear about what these numbers mean. Suppose this bell curve is a dance floor, and suppose there are exactly 10, 000 people crowded asshole to elbow on this dance floor. Then, the middle two boxes will have exactly 3413 people, each. And, the outer two boxes will contain exactly 1359 people each. Add these totals and subtract them from 10000 and the difference will be split between the two outermost boxes. 10000-3413--3413-1359-1359 = 456.

The best example of all is to think of this bell curve as a an upside down picture of Hoover Dam. Then, these numbers would represent the total weight of the hydrostatic pressure behind each section of its wall. The only real challenge you must face is being able to calculate the area of the independent sections by subtracting them from the cumulative sum of the distribution function.

What you are calculating is the "area under a curve"; or how many yard of carpet it would take to cover this dance floor. Area, is most often and most easily calculated by the formula AREA = WIDTH x HEIGHT, but this assumes a RECTANGULAR shape. This formula does not work for a triangle until you realize that every rectangle is made of two equal triangles. Hence the modified equation AREA = 1/2 WIDTH x HEIGHT, which is still easy to calculate because the change in length of the sloped side is still a straight line. If we change the sloped side of this wall to a semi-circular, most math students can still calculate the area based on the area formula for a circle, but it is definitely getting more challenging. Next, if we changed the curved wall to a parabola (like x-squared) then the precise area can only be solved by advanced integral calculus. And the slope, although no longer static, can be calculated. BUT, 'e' none as euler's constant (2.7173...) is based on infinite layers of change that are difficult to pin down even with integral calculus. Finally, the equation for the bell curve e^(-x^2) requires the calculation of an integral that is almost impossible to calculate. THIS IS WHY YOUR STATISTIC BOOK HAS LOVINGLY DISPLAYED EVERY POSSIBLE VALUE OF THIS CURVE'S AREA IN ONE OF ITS APPENDICES. But, if you are hell bent on pulling these numbers out of your ass then this is the least challenging way to do it:::(1) SUB-Divide the chart into as many smaller boxes as you can, and calculate the area for each 'micro-box' the way you would for a rectangle. (2.) Add the area EACH of the micro-boxes, and it will be a very accurate approximation of the actual area under the curve. As the number of boxes in your calculation approaches an infinite number of infinitesimally small micro-boxes, your approximation will become more and more accurate. This dilemma should serve to make you aware of the magic of calculus, but it is not something you should be sweating over.

Many of You are thinking of it backwards. 34.13% is the definition of what 1 standard deviation is. STANDARD DEVIATION is a method of describing how closely the data points adhere to the curve. From looking at the symmetrical shape of the bell curve, you can all tell that the average value (expected value) is smack dab in the center. But, we can stretch or squeeze this graph to infinite proportions without changing this central value. So, the next most important thing to calculate is the average distance each data point veers from dead center. The seemingly random fact that the average swerving distance of each data point from its center lane is + or - 34.13% is the feature which defines 1 standard deviation in this case scenario, and 1 standard deviation of + or - 34.13% is the key feature of the normal distribution curve.

[wealthywop]

it’s not a bad tutorial, so don’t let it distract u from the fact this help is better than none lmaoooo. stats final tomorrow morning and i’m just now learning les go

[eveunveils]

I literally didn't study at all so now I'm just watching videos to help me and my exam is tomorrow 🙃👌

[brentford]

Your ability to teach, enlighten, and simplify is > 2.58 sigma which now I know puts you in the 1%. THANK YOU!

[FlyGiiRlBubbleszz]

I leaving this vid just as confused as when i first clicked it

[arunavabhattacharya]

the most confusing tutorial i came across. Good Job mate. :)

[Chloe-dtvw]

So what you basically said is that I'm gonna fail?

[shaniquejoe]

Simple my behind! I understood a lil before this now I’m lost thank you!

[KitKat_Edwards]

Great video but how did you figure out the percentages? What if we numbered the bell curve with different numbers, would the percentages be the same?

[stephenmacdonald]

Great video. 

I have a question. Does your data have to be normally distributed to use these charts?
I have data grouped into categories (0, 1, 2, 3, 4, 5), almost 50% of the data points fall into category 0, so it is very skewed. I'm guessing this data won't be suitable for a control chart.

[chocolatecrud]

You should probably clarify a bit better that those percentiles of 34.13% correspond to a standard normal curve of a sample with a standard deviation = 1, and are based in reality, because a lot of people seem to feel like you're puling them out of thin air. I think calculus 2 would help a lot with this concept and those of later areas of general stats.

[goodwill]

Let us consider marks in statistics test of 100 students of a class. Where mean (mu) is 50, i.e. the average marks of the class is 50. And let us consider that standard deviation is 10.
So now, 68 students out of 100 will get marks within the range 40 to 60. (68% within the range of +, - 1 standard deviation) similarly 95 students out of 100 will get marks within the range 30 to 70 (in generic term 95% will fall under +, -2 standard deviations) and 99.7 students out of 100 will get marks within the range 20 to 80 ( in generic terms it's 99.7% will fall under +, -3 standard deviation).

[vinaykhandagale]

I like how it says 'explained simply' in first few frames.

[Mantroglodyte]

People get lost at the point with the percentages. Let me see if I can explain. Take a look at the x axis and imagine you have a tape measure. You can draw a length between the 0 and the 1. Let’s pretend that’s one foot. You can also draw one foot between the 1 and the 2. Right? Now imagine you have a scale. You take the slice of bell between the 0 and the 1. It will weigh something. Let’s pretend that’s one pound. If you were to weigh the slice of bell between the 1 and the 2 that is going to weigh less than a pound. There’s less stuff there, right? Consider that if you were to weigh the entire bell, it will weigh 100%. Just think about these concepts and I bet you get it.

Try not to get bogged down in the actual numbers. Just try and understand the concepts here. These seemingly random percentages are actual properties of the bell curve that has been figured out by statisticians. I personally feel the guy in the video described this shit rather clearly without getting lost in the weeds.

[donibrasco]

People getting confused the moment you jump to z-distribution while introducing normal distribution at the very basics like its curve that looks bell shaped. This is more of a giant leap of mankind to the moon for a child who is newly born and yet to see the moon. The improved version of this still misses the point, however, yes histograms run in the background of normal distributions.

[moody]

I’m in year nine and I just want to know what normal distribution, even distribution and un even distribution is for my homework *help me* 😪

[charmenerodrigues]

Great introduction to a very important probability distribution. However, growth of biological tissue (including here human height) actually fits a log-normal distribution, which means that the logarithm of height is a normal variable. A bit of a nitpick, but there you have it.

[padmasandhyasrikanth]

Are the numbers an integral of some complicated function? Because the %s are essentially area under the curve.

[IHeartEarth]

Thank you very much for this video, it was very explanatory. I finally get what I was calculating all this time in math class.