 Hello and welcome to the session. The given question says, the mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on we found that 3 observations were incorrect which were recorded as 21, 21 and 18. Find the mean and the standard deviation if the incorrect observations are omitted. So let's start with the solution. Here we are given that there are 100 observations so the value of n is equal to 100. The mean x bar of these 100 observations is given to us as 20. Therefore, 20 is equal to, to calculate the mean of 100 observations it's formula is summation xi i running from 1 to 100 upon 100. So this implies summation xi i running from 1 to 100 is equal to 20 into 100 which is equal to 2000. Also we are given the standard deviation. Let us denoted by sigma is equal to 3. It's formula is root over variance. So on squaring both sides we have 9 is equal to variance and variance is given by summation xi square i running from 1 to 100 upon 100 minus 20 square which is the mean of given 100 observations. So this implies 9 plus 400 taking this minus 20 square on the left hand side. We have summation xi square i running from 1 to 100 upon 100 or we have summation xi square i running from 1 to 100 409 into 100 which is equal to 40900. So let us denote this by second equation that is summation xi square i running from 1 to 100 is equal to 40900 as second equation. Now further we are given that wrong items 21, 21 and 18 are omitted. So this implies now the number of observations are 100 minus 3 observations that is 97 observations and now the correct mean is given by summation i running from 1 to 100 xi minus 21 minus 21 minus 18 and these 3 are wrong observations upon the number of observations which are now 97. Now from equation number 1 the value of summation xi i running from 1 to 100 is 2000 and we have minus 21 minus 21 minus 18 upon 97 and this is further equal to 1940 upon 97 which is equal to 20. Now let us find the correct variance it is equal to summation xi square i running from 1 to 97 upon 97 which are the number of observations if 3 observations are omitted minus the new mean which is 20 square. Now this can be written as summation i running from 1 to 100 xi square minus 21 square minus 21 square minus 18 square and the denominator we have 97 and these 3 we have subtracted because these 3 observations are omitted hence we have 21 square 21 square and 18 square minus 20 square is 400. Now from equation number 2 the value of this summation is 40900 minus 21 square is 441 minus 441 minus 324 upon 97 minus 400. So this is further equal to 8694 upon 97 minus 400 for a simplifying we have 409.22 minus 400 which is equal to 9.22 and thus the correct standard deviation is equal to square root of 9.22 which is equal to 3.036. Thus the correct mean is 20 and the correct standard deviation is 3.036. So this is our answer hope you have understood it take care and have a nice day.