 okay so we are back to measures of dispersion so in measures of dispersion we have four values that is range main deviation range main deviation standard and interquartile range okay so so we were seeing this one okay so this was our central tendency central tendency so here we had mean median or mode so this part and this part will be the dispersion so how it is dispersed above the mean and below the mean or above the median and below the median dispersion how it is dispersed from the central tendency okay so that is the central tendency and division so the first thing what we have is range sorry range so range is very simple when we have a data set how widely it distributed how widely it is distributed we can understand or we can calculate using this formula that is highest value minus lowest value if we have this data set the range is highest value minus the lowest value that is 18 minus 5 that is 10 this is the dispersion value okay that is measure of dispersion so for just we can take the mean value that is 5 plus 7 plus 8 plus 10 plus 15 plus 18 divided by 6 so 15 20 30 33 43 48 58 66 that is 66 by 6 that is 11 so the central tendency is 11 and the dispersion is 10 so it says that on an average it has 11 it is coming at the center and it is deviated 10 values from the center sometimes the values are different so it may not give the exact result because of the value because we are taking a very small number of data set but when we are taking a very high number of data set that is around 50 values or 100 values it will give almost a precise measurement because the central values that is central tendency 11 and dispersion will be coming like this if we add some values that is 11 plus 10 21 and 11 minus 10 so it will give negative value since we have a very small number of data set we are getting this one anyway this is the calculation you don't worry about it is not getting the actual number it is just an example with a low data set so this is the dispersion that is the range first one range I simply showed you the central tendency value that is 11 okay this one how we calculate mean so if you take median it will be 10 plus 8 by 2 that is 18 by 2 that will be 9 mean median there will not be any mode for this one because 578 10 15 18 a different number okay so that is all about range okay the next we have the mean deviation mean deviation is the formula is x bar this is mean sigma x bar minus x i i means the individual value okay so for getting getting this mean deviation for this data set this is the data set what we do is first we calculate the mean that is 2 plus 4 plus 6 plus 8 plus 10 30 by a number of observation 5 is 6 okay so then we subtract each value subtract each value from mean that is we subtract 2 from mean 4 from mean 6 from mean 8 from mean and 10 from mean so we get actually the negative 4 or minus 4 or minus 2 0 2 and 4 but we are taking the absolute value so this negative symbols will go off so we get the absolute value so we multiply that is sigma sigma so this is sigma so we multiply this sorry not multiplication adding so we add this 4 plus 2 plus 0 plus 2 plus 4 so 12 is the mean deviation okay so this is how we calculate mean deviation so I'll coming to the standard deviation the difference is because we are we are we were using the absolute value because of the sign where neglected so to avoid that problem what we do is we square it off we square it off that is we square the values we square the values to nullify it what we do is we take the square root we'll take the square root divided by n so here we I forgot to tell you that we were supposed to divided by 5 that is 12 by 5 you get 2.5 was the mean deviation okay I forgot to tell you we were supposed to divide it so we get mean deviation 2.5 so the standard deviation in order to avoid that this sign problem we square it off then we take the square root we take the square root sigma is there anyway and we divide it with the number of observation so what we do is 4 square plus 2 square plus 0 plus 2 square plus 4 square by n so 16 plus 4 plus 0 plus 4 plus 16 by n so root of 20 20 40 by so by 5 is 8 root 8 is root 9 is 3 so it will be come around 2.8 okay so this is the standard deviation standard deviation is the most accurate one than the mean deviation mean deviation we take the absolute value but here we take the actual value but we square and we'll take the square root to nullify that squaring effect we divided by n so we get 2.8 that is the standard deviation so let's back to the in the cocktail range okay in the cocktail range is the range between two cocktails that is if we have a data set like this that is 1 2 3 2 15 we are dividing it as four cocktails that is cocktail number 1 cocktail number 2 cocktail number 3 and cocktail number 4 okay you don't worry about this Q3 this is this one this is Q4 this is Q3 this is Q2 and Q1 don't worry this is the lowest value this is the highest value and we take the median value okay so for in the cocktail range we take median first so this is 15 number so we take the exact middle value that is 8 that is a median value okay so next we take the lower median that is the lower half 1 2 7 we get the median value is 4 that is a Q1 that is a Q1 cocktail number 1 okay so that is a median value of lower half and the median value of upper half that is 9 to 15 we take 12 because this is the middle value that is Q3 okay so this is Q1 is 4 and Q3 is 12 okay so this is the median this is highest value this is lowest Q1 median Q3 and highest value don't worry about Q2 and Q4 Q2 and Q4 is there but you don't worry you worry about only this formula Q3 and Q1 that is IQR is equal to quartile 3 minus quartile 1 that is 12 minus 4 that is 8 okay so if you divide the data set as lowest Q1 median Q3 and highest value and we find out the median value we find out the lower half median value we find out the upper half median value so we get Q3 and Q1 so subtract we get the inter quartile range okay so that's how we finishing the measures of dispersion okay so let's sum up all these if you go through articles you can see that the data is represented in this format mean plus or minus standard deviation mean is always with standard deviation and median is always with IQR because while calculating IQR we are taken median while calculating standard deviation with taken mean so any article 99 percentage of the article you will be seeing either two values that is mean plus or minus standard deviation that is above the mean and below the mean above the median and below the median so these are the measures of central tendency and measures of dispersion so this is the measure of central tendency and this is a measure of dispersion okay so measure of dispersion is range mean in deviation and standard deviation and inter quartile range measure of central tendencies mean median and mode mode we rarely used you can neglect it but write it for example so when in articles you can see mean and standard deviation or median at inter quartile range when the data set having out layer we go for median if you are taking median you should go for IQR as a measure of dispersion if you are taking mean you should take standard deviation as a measure of dispersion so these two are measure of central tendency and this is measure of dispersion okay thank you