 Hello and how are you all today? My name is Priyanka and the question says find the mean variance in standard deviation using shortcut method. So here let us draw a table to simplify our solution. Now here we need to find out firstly xi and that we know is lower limit plus upper limit divided by 2. So let us quickly calculate it. Now here we have assumed the mean as 92.5 and the difference of each consecutive xi is 5 so we will take h as 5. So what we have over here is we have assumed mean that is a is equal to 92.5 and we have h that is the difference between the consecutive xi's that is equal to 5. Now what we need to do is we need to find yi that is xi minus a upon h. So it will be minus 4 minus 3 minus 2 minus 1 0 1 2 3 4. Then we need to multiply fi and yi and we will get minus 12 again minus 12 minus 14 minus 7 0 9 12 18 again 12. Then find out yi square and that is 16 9 4 1 0 1 4 9 and then 16. Now we need to multiply fi with yi square and on doing so we have 48 that is 3 into 16 4 into 9 giving us 36 7 into 4 28 7 into 1 7 15 into 0 0 9 into 1 9 24 9 into 6 giving us 54 and 3 into 16 giving us 48. Now find out the sum that is coming out to be 254 here 6 over here and the sum of all the frequencies are 60. So what we need to find out here is we need to find out the mean the variance and the standard deviation. So let us first find out the mean and it is a plus h into summation fi yi upon summation fi and that is further equal to we have assumed mean as 92.5 so we have 92.5 plus 4 into summation fi yi was 6 divided by summation fi that is 60. So we have on calculation the value of mean as sorry here h was not 4 but 5 so it is 92.5 plus 0.5 giving us 93 as mean. Now we need to calculate variance and now substituting we have 5 the whole square upon 60 the whole square into 60 into 254 minus 6 the whole square that is 25 upon 3600 into 15 240 minus 36 that is further equal to 25 upon 3600 into 15204 that is further equal to 105.5 2. Now we need to calculate standard deviation and that is under the root variance and that is under the root 105.5 2 and that is 10.27 approximately right this was also an approximate value so we can write that the answer here is mean is equal to 93 variance is equal to 105.5 2 standard deviation as 10.27 right so this ends the session hope you enjoyed and understood the whole activity the whole question well and have a nice day