He never explained what the mode would look like on the second symmetric graph, but I think the video is good to grasp the idea of how mean and median shape the probability distribution function, or how they look like based on the shape.
Variance is equal to E(X^2) - (E(X))^2. Standard deviation is the square root of variance. So first find E(X^2) by taking the integral in your distribution bounds of your function p(x) times x^2. Then find expected value E(x) by taking the integral in your distribution bounds of p(x)*x. Then simply find variance by the formula stated and take the square root.
Adam Kretz - He said a simple thing in a complicated way. To calculate the mean, you simply add up all of the values in your data set and divide it by the number of counts in the data set. For instance, imagine we have 4 people with heights of 5’, 5’, 6’, and 6’. If you add that up, it is 22’ of total height. 22’/4 people = a mean (average) height of the people in that data set of 5.5’.
The mean as he describes it is actually something known as the expected value (same thing in probability). Expected value is calculated as the summation of all x values times their "weightage" or the y-axis representing probability in this case.
@@StrategicWealthLLC The way Sal describes Bruce's problem is by knowing that 5' occurs 50% of the time and 6' the other half of the time. Hence, the expected value or mean is 5'*.5 + 6'*.5 = 5.5'
He's wrong. The mean is what makes the area equally divided into two parts and not the mean. Think of what he said, "Mean is like a fulcrum", the two sides will balance only if the area of both sides are equal(If you know decent physics, you can prove this easily). Thereby contradicting what he said about the median. Let me know what you think!
Actually, the video is correct (but perhaps doesn't explain it well). For why the median is equal areas: Think of this graph as a smoothed bar graph, where the height is the count of observations. The median adds up these counts and makes each side equal. For why the mean does not necessarily result in equal areas: the mean is not just about numbers of observations on each side (which is what the area represents in these graphs) but also their values (their location on the axis something that isn't well-presented here because they don't label the axes) A single point that has a very large or small valueshas a big influence on the mean. The way I explain this is suppose this is a distribution of people's wealth. Median would be the value where half the people are above and half below. The mean would be to pool everyone's money together and then divide it up equally. So, if your data includes Jeff Bezos, he is a single person (i.e. not much area in this graph) very far to the right (extremely wealthy), and would pull the mean wealth higher while median would be relatively unaffected by one person.
By applying decent physics as you noted, if you put a fulcrum to balance something, it actually takes the weight of substances into account and not their area. And it is not necessary for weight to be directly proportional to area because of a simple concept called density. The topic presented here is about density curves, where you plot a graph between the frequency of a data-point in y-axis and the data-point itself on the x-axis. Now, as the frequency of data-points can vary, so does the density of the curve; therefore a typical density curve may have areas of less data points (less dense) and areas of more data points (more dense) wherein the magnitude of these areas are taken as equal. The median is that point where the average density is equal on both sides and therefore Mr. Khan gave us an analogy of fulcrum balancing the curve.
@@mnh3088 By applying decent physics as you noted, if you put a fulcrum to balance something, it actually takes the weight of substances into account and not their area. And it is not necessary for weight to be directly proportional to area because of a simple concept called density. The topic presented here is about density curves, where you plot a graph between the frequency of a data-point in y-axis and the data-point itself on the x-axis. Now, as the frequency of data-points can vary, so does the density of the curve; therefore a typical density curve may have areas of less data points (less dense) and areas of more data points (more dense) wherein the magnitude of these areas are taken as equal. The median is that point where the average density is equal on both sides and therefore Mr. Khan gave us an analogy of fulcrum balancing the curve.
this is very poorly explained, not even talking about the lack of information I wish you good luck. Try to help people, why are you doing theese kind of videos?
This was a very simple, yet helpful explanation of density of data. Thank you.
This was a really nice way of explaining it in simpler terms. Thank you for your help!!
Simple and awesome explanation ❤️
Very objective and clear explanation! Thank you
What if you combine 1st and 2nd graphs and compare mean, median & mode???
He never explained what the mode would look like on the second symmetric graph, but I think the video is good to grasp the idea of how mean and median shape the probability distribution function, or how they look like based on the shape.
there would be 2 modes, since both sides are symmetrical. That is why the second graph is called "bimodal symmetrical".
And if it was trimodal, then it would have 3 modes, etc
Thanks for the video, it's really helpful
Why do we calculate standard deviation by using mean? Namely, why dont we use mode instead of mean?
Ooh synthesis.
nice its so good. Porps on 7m subs
What is an example of negative skew?
Negative skew is the same as left-skew, because the tale is going towards the negative side/skewed negatively. And the opposite for Positive-skew.
Thank you
How to calculate the standard deviation of a non-normal distribution?
Variance is equal to E(X^2) - (E(X))^2. Standard deviation is the square root of variance. So first find E(X^2) by taking the integral in your distribution bounds of your function p(x) times x^2. Then find expected value E(x) by taking the integral in your distribution bounds of p(x)*x. Then simply find variance by the formula stated and take the square root.
thanks alot
How about the mode?
the mode is always just at the highest point. If you think about it, highest probability point will always have the most similar values.
Swag Fzce so you’re saying a mode is considered a median?
"The mean is you take each of the possible values and you weight it by their frequencies and you add all of that up"-very confusing i.m.o.
I didn't get that too
Adam Kretz - He said a simple thing in a complicated way. To calculate the mean, you simply add up all of the values in your data set and divide it by the number of counts in the data set. For instance, imagine we have 4 people with heights of 5’, 5’, 6’, and 6’. If you add that up, it is 22’ of total height.
22’/4 people = a mean (average) height of the people in that data set of 5.5’.
other than simple mean or average there is weighted mean too in which weights are assigned to the values and then u calculate the average
The mean as he describes it is actually something known as the expected value (same thing in probability). Expected value is calculated as the summation of all x values times their "weightage" or the y-axis representing probability in this case.
@@StrategicWealthLLC The way Sal describes Bruce's problem is by knowing that 5' occurs 50% of the time and 6' the other half of the time. Hence, the expected value or mean is 5'*.5 + 6'*.5 = 5.5'
just a quick correction. today i drank exactly three glasses of water. down to the subatomic level baby!
Watching this because of AP Stats
Same
so thankful for YOU lol
thankyou thankyou thankyou !!!!!!
Thanks, really good explanation
Tysm
He's wrong. The mean is what makes the area equally divided into two parts and not the mean. Think of what he said, "Mean is like a fulcrum", the two sides will balance only if the area of both sides are equal(If you know decent physics, you can prove this easily). Thereby contradicting what he said about the median. Let me know what you think!
can i ask something?
i do agree with you. there is something wrong in his definition about median!
Actually, the video is correct (but perhaps doesn't explain it well). For why the median is equal areas: Think of this graph as a smoothed bar graph, where the height is the count of observations. The median adds up these counts and makes each side equal. For why the mean does not necessarily result in equal areas: the mean is not just about numbers of observations on each side (which is what the area represents in these graphs) but also their values (their location on the axis something that isn't well-presented here because they don't label the axes) A single point that has a very large or small valueshas a big influence on the mean. The way I explain this is suppose this is a distribution of people's wealth. Median would be the value where half the people are above and half below. The mean would be to pool everyone's money together and then divide it up equally. So, if your data includes Jeff Bezos, he is a single person (i.e. not much area in this graph) very far to the right (extremely wealthy), and would pull the mean wealth higher while median would be relatively unaffected by one person.
By applying decent physics as you noted, if you put a fulcrum to balance something, it actually takes the weight of substances into account and not their area. And it is not necessary for weight to be directly proportional to area because of a simple concept called density. The topic presented here is about density curves, where you plot a graph between the frequency of a data-point in y-axis and the data-point itself on the x-axis. Now, as the frequency of data-points can vary, so does the density of the curve; therefore a typical density curve may have areas of less data points (less dense) and areas of more data points (more dense) wherein the magnitude of these areas are taken as equal. The median is that point where the average density is equal on both sides and therefore Mr. Khan gave us an analogy of fulcrum balancing the curve.
@@mnh3088 By applying decent physics as you noted, if you put a fulcrum to balance something, it actually takes the weight of substances into account and not their area. And it is not necessary for weight to be directly proportional to area because of a simple concept called density. The topic presented here is about density curves, where you plot a graph between the frequency of a data-point in y-axis and the data-point itself on the x-axis. Now, as the frequency of data-points can vary, so does the density of the curve; therefore a typical density curve may have areas of less data points (less dense) and areas of more data points (more dense) wherein the magnitude of these areas are taken as equal. The median is that point where the average density is equal on both sides and therefore Mr. Khan gave us an analogy of fulcrum balancing the curve.
Love from Pakistan.
israr karim well love from Syria
Pakistan sucks Muslim (miao)
@@fightinglight65-gamingandm29 Khan himself is a Muslim you idiot.
ترجمه عربي
I thought the middle part is the mean of the data. Let me know.
nope it's always been median.
@@professorx4547 It is the mean, the median and the mode. All three.
Statistics?!
No, Algebra
Astrology
How the F does Sal know shit about every topic out there and finds a really good way to teach it?
no one:
me watching this video: OnE DiReCtIoN
nutz dees
this is very poorly explained, not even talking about the lack of information
I wish you good luck. Try to help people, why are you doing theese kind of videos?
Understand that this guy has 4.5 Mil subs and all of those are from helping people. Your negative comment isn't helping anyone either.
why coz u couldn't understand it ??
@@pranavm.9513 understand this was commented a year ago and he probably wont respond :/
@@CatgirlSmok
Yeah now that i look at it.
First
First lol