STATISTICS- Variance and Standard Devation

Key Takeaways

hello all my name is Krishna and welcome to my youtube channel now in this particular video I'm going to discuss about a very important topic which is called as variance and standard deviation and we understand this topic with respect to statistics and machine learning also in my previous video I have already explained you about main median and mode and I'm going to take the same example of sample of heights so this is my sample of distribution these all are basically in centimeters and suppose if I find out the mean as 160 3.5 now what does variance how to calculate variance will try to understand how to calculate standard deviation and then we'll also understand what is the importance of variance and standard deviation so to begin with if I want to calculate the variance the formula is 1 by n summation of I is equal to 1 to n X of I minus mu whole square so this mu is basically my mean ok so I am going to use this now when I compute this variance we will try to understand what does variance and standard deviation specify the next formula is basically standard deviation is equal to root of fees now suppose after calculating this I hope you can calculate it by using all this values and suppose here I get basically 10 suppose my standard deviation is basically 10 let me specify what this standard deviation basically specify standard deviation helps us to find out the spread right in our distribution how the spread is with respect to different different values that are present over here suppose my mean over here is 160 3.5 now if I see my standard deviation is 10 again guys I just have approximately written it you can calculate it there will be some different value it's fine but I'm just going to consider 10 to make you understand so what this basically says if I go to the right hand side of this mean which is basically my one standard deviation see this this value is basically my if I consider this this is my one standard deviation okay one standard deviation to the right one standard deviation to the left okay similarly if I consider this this is my two standard deviations similarly if I consider this this is my three standard deviation okay so this basically indicates that if I move one point to the right my next value that will be probably in one standard deviation is somewhere around 164 point five okay because I'm adding up ten into this value similarly if I go one step right again it will be sorry it should not be 164 it should be 173 0.5 okay and similarly if I go here it'll be 183 point five then one ninety three point five okay so 193 for him five is outside the third standard deviation similarly if I go to the rat left okay so this basically indicates it will be 150 three point five one forty three point five and one thirty three point five because if we are going to the left that basically means you are subtracting it because this is my median right if I go to the right that value basically increases if I go to the left that value basically in decreases and this is again this curve is basically called as Gaussian distribution guys why I am creating this shape why this will form a bell shape because understand this height usually follows a normal distribution or Gaussian distribution and who is saying this I am NOT saying it these are basically explained by domain expertise people who are basically measuring height height weight and other parameters like age and all right so this is what this standard deviation specifies it specifies the spread of the value within the distribution and this is basically my spread when concerned and when I'm considering one standard deviation 1 standard deviation spirit is around 10 value so if I move to the right it will always get added as 10 if I move towards the left it will always be you know subtract 10 okay which is my standard deviation and this was all about radians and standard deviation and this is also very very important guys because let me consider an example for you let me explain it okay you will be seeing again I'll take the same feature H I'm based on this particular age feature also if you try to see the values in your data set okay in your data set so suppose your values are like 23 24 27 30 to 31 26 and if you try to see this distribution in the form of histogram okay and then you construct something called as probability density function you will be finding that you'll be forming a shape like this which is basically called as Gaussian distribution again what will be the importance of that I will be explaining about about that in the next videos because Gaussian distribution follows some properties and that properties we can also apply to this particular data set for our statistical analysis so this is the important of variance and standard deviation to know that okay so I'll be discussing more about this in my next video I hope you like this particular video please do subscribe the channel if you have not already subscribe I'll see you all in the next video have a great day thank you one and all [Music]