 Hello friends and how are you all today? The question says find the mean and variance of for the following frequency distribution. Now here we are given the classes as well as frequencies and we need to apply the shortcut method to find out the mean and the variance. Now for the shortcut method first of all we need to draw a table. Now here we are given the classes as well as the frequencies. First of all we will be finding xi which is lower limit plus upper limit divided by 2. So here it would be 5, lower plus upper divided by 2, here it will be 15 and so on with the difference of 10 we will proceed on. Now we need to find yi. Now to simplify our calculation we take the middle value as our assumed mean. Now from each xi we subtract the yi sorry the assumed mean and then we will be dividing it by the difference and that is 10 to obtain yi. So it will be 5 minus 25 giving us minus 20 divided by 10 giving us minus 2 head 10 is h that we take. So we have here minus 1, 0, 1 and 2. Now to find out yi fi we will be multiplying these two terms and we will be getting minus 10 minus 8, 0, 16 and 12. Then yi square that is 4, 1, 0, 1, 4 and then multiplying it by the frequency again. So we have 20, 8, 0, 16 and 24. Let us sum them up. Now on finding out the sum we have summation fi yi square is equal to 68. Summation fi yi as 10 and summation fi as 50. Now here we have taken the assumed mean as 25 which is denoted by the letter a and we have edge. The difference by which we have divided to obtain yi is taken as 10 that is the difference between the consecutive terms of yxi. Right now to find out the mean we have the formula as a plus h into summation fi yi divided by summation fi. On substituting we have the answer as mean is equal to 25 that is the assumed mean plus 10 into summation fi yi is 10 divided by 50. So we have the answer as 25 plus 2 that is 27. Now we know the formula for variance it is h square upon summation fi the whole square into now substituting the values we have h as 10 the whole square it will be 50 the whole square into fi is 50 fi yi the whole square is 68 minus 10 the whole square. On simplifying we have 100 divided by 2500 into 50 into 68 giving us 3400 minus 100 the 10 the whole square giving us 100 simplify it so we have 21 upon 25 into 3400 minus 100 that is 3300 and the answer is 120 sorry 132 we can write the answer to the session as mean is found out above as 27 and the variance as 132 right this ends my session hope you understood it well and have a nice day