 Hello friends and how are you all today? My name is Priyanka and I shall be helping you with the following question. It says find the mean and variance for each of the following data. Now here the first data which is given to us is 6, 7, 10, 12, 13, 4, 8 and 12. Now to find out the mean and variance let us firstly be well versed with their formula. We can calculate mean of a data which is denoted by this symbol by dividing the sum of observations by the number of observations. That is x bar is equal to 1 upon n summation xi where i is equal to 1 to n where n is the number of observations and observations are the given values which we call as x1, x2, x3 and so on. And then for calculating variance that is denoted that this symbol is equal to 1 upon n summation xi minus mean the whole square where i is equal to 1 to the number of observations that we have. Right? So the knowledge of these two formulas are the key ideas to work this question. Now let us start with the solution. Here the observations are let us put them into a tabular format. Now here we have the xi that is the observation as 6, 7, 10, 12, 13, 4, 8, 12. What we need to do is first of all we need to find out the sum of these observations and not adding them we have the sum as 72. Right? So let us firstly find out the mean that is equal to 1 upon n, n here are. So we have 1 upon n that is 8 summation xi that is 72 and on solving it we have the mean equal to 9. Right? Now to calculate the variance firstly we need to subtract the mean from, now here we have 9. So we need to subtract from each observation 9 and we have the answer as minus 3, minus 2 and 10 minus 9 gives us minus, sorry plus 1. Then we have further as first we had minus 3, minus 2, 1, 3, 4, minus 5, minus 1, then 3. Now we need to find out the square since we need to find out summation xi minus mean the whole square. So let us first find out xi minus mean the whole square and then we will find their sum. So we have here minus 3 the whole square as 9, minus 2 the whole square as 4 and so on. Now let us find out the sum and the sum is coming out to be 74. So we have the variance as 1 upon n that is 8 summation xi minus mean the whole square and that is 74. Where n is equal to 8 in summation xi minus mean the whole square where i is equal to 1 till 8 is equal to 74. So on calculating here we have the answer as 9.25 as the variance. So let us write down the answer one again. This is one again it is mean is coming out to be 9 whereas variance is equal to 9.25. This completes the session hope you understood the construction of this table and the procedure well bye for now.