 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says from the prices of shares X and Y below, find out which is more stable in value. So in the table given below in the first row we have the prices of share X, in the second row we have prices of shares Y. So let us start with the solution to this question. Now for determining which share is more stable in value, we have to find both their variance from the variance which ever is lesser value of variance is said to be more stable. So let us see how to find out the variance. Step one is calculate the mean of a data denoted by X bar that is X bar is equal to 1 divided by n into submission X i where i goes from 1 to n where n is the number of observations. Now step two is we find X 1 minus X bar X 2 minus X bar X 3 minus X bar and so on till X n minus X bar. Step three is to find X 1 minus X bar the whole square X 2 minus X bar the whole square and so on till X n minus X bar the whole square. Step four is we find their sum that is we find submission X i minus X bar the whole square i goes from 1 to n then step five is to find out the variance that is sigma square equal to submission i goes from 1 to n of X i minus X bar the whole square divided by n. So now like this we make a table this is for shares X and this is for shares Y they are the X i's given to us in the question they are the Y i's given to us in the question we have to find out X i minus mod X or X bar and similarly we find Y i minus Y bar then we find X i minus X bar the whole square and here also we find out Y i minus Y bar the whole square. So let us find out X bar we know that X bar that is the mean of the data is equal to into submission X i where i goes from 1 to n this is the standard formula for the mean. So let us sum up all these X i's and similarly we mean of Y will be equal to 1 by n submission Y i where i goes from 1 to n. Here also we sum up all the Y i's we see that submission of X i's is 510 and submission of Y i's is 1050. Now we have to find out X i minus mean of X. Now we see that we have to find of mean of X that will be equal to 510 divided by now number of observations that is n is equal to 10 so mean of X is equal to 51 similarly here we see that we get 1050 divided by 10 and that is equal to 1005 this is 105 so mean of X is 51 and mean of Y i's is 105 minus 10 minus 2 we find out their square is 9 square of 1 is 1 here then 0 X bar the whole square and Y i minus Y bar the whole square. So we have summed them up we see that this sums up to 150 and this sums up to 40 finding their sums that is this we find out the variance that for shares X variance sigma square is equal to submission i goes from 1 to n X i minus whole square divided by n we simply put in the values here and we get 350 divided by 10 that is equal to 35 so variance for shares X is 35 only for shares Y variance that the sigma square is equal to submission Y i minus Y bar the whole square i goes from 1 to n divided by n that is equal to 40 divided by 10 and that is equal to 4 now we see that to compare the variability we have to calculate their coefficients of variation now coefficient of variation for X is X divided by X bar multiplied by 100 we see that sigma sigma square is equal to 35 so this implies that sigma is equal to square root of 35 divided by that was 51 multiplied by 100 now this is equal to by 100 divided by 51 i 100 and 90 divided by 51 7.6 so coefficient of variation for X is 11.6 now we find out coefficient of variation for shares Y that is again sigma for Y divided by mean of Y that is Y bar multiplied by 100 will be since sigma square equals to 4 so sigma will be 2 so here we have divided by now mean for Y is 105 so this multiplied by 100 that is 200 written 5 this is 2 by 105 into 100 because sigma Y is 2 mean of Y i's is 105 multiplied by 100 so we have 200 divided by 105 that is approximately equal to 1.9 we see that coefficient of variation shares Y coefficient of variation answer to this question is Y so I hope that you understood the question and enjoyed the session have a good day