So in this question, were given a pie chart with a bunch of values and were asked to calculate the mean and the standard deviation for the sample. So to do that, let's go ahead and make our frequency distribution charge. So let's start with. Since this is a grouped data, we're going to take the midpoint off each class as our value off X. So we have X. The midpoint off 0 to 4 hours is too. 5 to 9 is seven 10 to 14 is 12 15 to 1917 22 24 22 25 to 29 is 27. And for 30 plus hours we're told to list the midpoint as 32. So we have our values off X. Now we're going to put our frequencies in. So we have five, 12, 24 17, 16, 11 and five. So we have all of our X and our frequency values. Now we're going to compute x times f. We have X f and for that we're going to get five times two is 10 12 times seventies 84 24 times 12 is 288 17 time 17 29 22 times. 16 3 52 21 20 Picture 27 27 times 11 He had 297 and then 32 times 51 16. So we get X times have over here, and our formula for the mean is basically the some off next times f over our number off values. So we're basically going to sum everything in this column and in this column, and we're going to computer mean? And so in this column was some this 1480 number of values. We have this 19, so we take one for 80 divided by 90 which gives us the sample. Mean off 16.44 So that's our first answer for the second one. We need to find standard deviation. So let's go ahead and expand this table out Basically what we have to calculate here. IHS X minus the main affects. Then we're going to square that remember going to multiply that by them frequency, and from there we can calculate the sample Standard division. The formula for the standard deviation is basically the some off X minus X squared times F divide by and minus one and the square root off this whole thing. So let's go ahead and calculate this value. This one we know is 89. So this value let's go ahead and calculate from this column over here. So just to remind ourselves the mean effects waas 16.44 eso to calculate this we take X which is two minus 16.44 Then we square it and we multiplied by five. Which gives us 1042.56 Yeah. Now here we have seven minus 16.44 squared times 12. 10 69 0.3632 Then we have 12, minus 16.44 squared times 24 Just 473 point 1264 and 17 minus 16.44 The whole thing squared times the frequency which is 17. 5.3312 Then we have here 22 minus 16.44 squared times 16 Just 494 points 176 Then we have 27 minus 16.44 squared times 11 12 to 6.6496 Then our last value 30 to minus 16.44 squared times five 1 to 10.568 And the sum of all of these values gives us well, you off. It gives us 55 to 2.24 So we're gonna put that into our standard deviation. So we have 55 to 2.24 He divided by n minus one. And then we take the square root and we get for our standard deviation 7.877 approximate to three decimal places, which gives us the mean and standard deviation from this sample.