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Do the following:

a. Group the data as indicated.

b. Prepare a frequency distribution with a column for intervals and frequencies.

c. Construct a histogram.

d. Construct a frequency polygon.

Repeat Exercise 2 using six intervals, starting with 39–48.

SEE THE GRAPH

Multivariable Optimization

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this question gives you a huge table of data 80 points and asked you to sort it into six bins, starting from 39 with the length of tents. The first been will be 39 to 48. And the next will be, Ah, 49 to 58. And so on, um, is a lot of numbers. I've already done this on paper out before I started this video. Um, so I'm just gonna sort of give you an example of what I was doing. I would start with the been 39 to 48 I'd go through the whole table and pick out the numbers that fall in that been. So for the first range, um, I found a 46 and then a 48 Um, a 42 a 39 and 45 a 48 and so on. So I get to do that for every single been all six of them, and I'm not gonna do it here, cause that would take forever. Um, but that was just the general idea. Um, select the range pick out from the big clump of data. The numbers that fall into that range. Um, the next part of the problem. Ask you to make a frequency table, and this is where it gets more or into the date of the frequency table. A friggin potato consists of two things. First column is a column of ranges That means all the ranges that we were using toe group our data. We don't want to just list those. So the ranges that we ended up using were 39 to 48 49 to 58 59 to 68 69 to 78. And, well, 79 to 88 end 89 to 98. So these air are ranges. And now the next column is frequencies. That's f uh, is frequencies is just the number of data points that came up in each range. So we found six in our first range. Um, we've had 13 in her second range. Um, you could pick up 20 from the third 19 from the fourth 13 and then nine from our last. So these were the frequencies that I found as I was going through a doing, um, that process next, it asks us to make a history. Graham. Now hissed a gram. Um, I'll draw some axes here. This will be my wife Existence with my ex X is and what I'm gonna do first is label where my bins air gonna go bends again or my ranges. Um, how we group the data. Um, What I'm gonna do is I'm gonna have my bins include the left endpoint. That is, if this is 39 this here is 49. This boar here is going to include 39 but not for denied. And that's what we want for our for our date of the Wave grouped, it sold 39 49 59 69 79 89. And our last point. The end where we're stopping is 99. So let's go. Let's go through and look at this. Oh, I need to set my why. Scale, Teoh. I think I'm are. Max is 20. So put that at the top Here, 20 And in all this, a 10. Um And then we'll have five is there and 15 is there. And hopefully we'll be able tow toe. Make some sense out of this. So first, our first been 39 to 48 we found was six. It's just above five right there, and I'll label it just to make it clear. Then we found 13. So it'll be up here. Um, then we found 20 between 59 68 all the way up here. And these aren't perfect. It's a hand drawn graph, but he gives Thea the reader a little bit of clarity about what's going on with this data. Next is 19 of just south of 20 Here. Um, we also have our 79 to 88. We found 13. So again, that will be right here. And finally, our last been we found nine. So just south of 10 right there. The last thing this problem asks is to make a frequency polygon. Now, frequency polygon is just essentially, um, a shape that can overlay a hist a gram. Um, that connects sort of the mid points of each of its bar and shows the the general distribution sort of in a a low clarity. So I'm gonna start the way you start is sort of the, uh, a good way to start is the halfway point on the left end of the left. Most bar, Um, and then you go up to the midpoint of the first, then the midpoint of the second, and so on. You connect all of these, and I'm not drawing very straight, but that's OK. And then you connect the midpoint of the top of the last bar with the midpoint of the right side of the last bar, and you'll have your frequency polygon. And so this is what your final answer is gonna look like.