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Problem 3 Medium Difficulty

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 1 using eight intervals, starting with 0–19.

Answer

SEE THE GRAPH

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Video Transcript

this question gives us a big table of 36 data points and asks us first to group them into ranges. The range is it wants start like this, 0 to 19 and then it asks for eight of them. So the next will be, Ah, 20 to 39. And so, uh, so let's start the way I'm gonna do this. I'm just gonna go through this table once for every range and pick out the numbers that are in the range that I'm looking for. So first for 0 to 19 I'm gonna go through and we'll find a seven. A 12 2 and 13. And I'll admit I've actually already done this. I've got to solve it down on paper. But it's the same process. So for each range and going through the table and picking it out the next 1 2039 will find that there's 26 29 37 38 32 Um, our next been or ranges 40 to 59. Where will find a 44 a 50 a 43 and a 40. Next, we want, um 50 air 63 60 to 79 and we'll go through and find a 73 and other 73 65 a 79 and a 74. Getting our next business 80 to 99 will find in 82 in 85 82 again 99 85 in 95 90 86 then 84. Next, we'll look at 100 to 1 19 here will find a couple more off on one of five. One of six and then 100. Um, Well, look next at 1 20 to 1 39 Here we'll find 1 29 1 26 1 37 No, 1 21 And finally we'll look at our last Bendis or 8th 11 40 to 1 59 which would encompass 1 41 and 1 47 And so these air are our data grouped into a bunch of ranges. Next, it asks us to make a frequency table that we're going to eventually make a hist a gram and to facilitate that will make a frequency table. Um, figures The table consists of a column of ranges, so we'll just write down the range is that we had, um 0 to 19 20 to 39. 40 to 59 60 to 79 80 to 99 100 to 1 19 1 20 to 1 39 and 1 40 to 1 59 Those were all eight of our ranges, and then we The next column is frequency. I'm just gonna abbreviate. That is F frequencies. Just the number of data points that, uh, found themselves in this range. So for our 1st 1st been we had four, then we had five. We had four again. And then another five in between 80 and 99 we had nine data points. Um, 101 1983 After 1 20 we had four. And then the last one we had to So the next one this question asks us to make a history, Graham. Um, so let's go ahead and do that. We're going t o. I'm gonna draw some axes. Here's my Y Axis is my X axis, and I want to split this up into bins. And the way I'm gonna do that, I'm gonna have the left endpoint be included in the bin. So this would be zero and the next point will be 20. And so the bar that's here will be 0 to 19. Little include the left endpoint, but not the right end point. So I have 20 40 60 and I want to leave myself enough room heating 100 1 20 1 40 And our last point is 1 60 All right. And so now I have to decide on my why access. I think I'm gonna want this scope to 10 and we'll go by twos. 246 and eight. And now it's time to start plotting. So here, what we'll do is we'll go to our range. We have 0 to 19 right here, and we'll plot. How many there were. There were four between zero and 19. So make a bar that's for high. There were five between 20 and and, uh, 39. So we'll make it another bar that's has a height of five. Next bar will be four between 40 and 59. Then between 60 and 79. There were five. So up here between 80 and 100 there were nine. That's gonna be a big jump up here. Between 101. 19. There were three so it drops down and this doesn't have to be perfect. Obviously it's hand drawn, but it should give you a clear idea of what's going on with the data. Between 1 2139 there were four. So it will be here again in between 1 41 59 There were two. So right down here Next we're asked Teoh, make it frequency. Polygon, A regular polygon is basically just hissed a gram. But you've drawing a line to connect all the mid points at the top of each bar. Um, and you end up with, uh, a Poyang that is sort of describes the distribution of these data points. So on the left, I'm going to start at the midpoint of the bar that we're every are given. So this bar is four high. I'll start it too, on the Y axis and then go up to four at the midpoint of this bar than ever over the five, down to four. Back up to five, up to nine, down to three. And let me make this a little bit neater. Down to three. Up to four. Down to two and then ended up at one and so you can shade it in if you choose. But this is what a frequency polygon will look like, and that's your final.