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Problem 2 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.
Use seven intervals, starting with 30–39.
$\begin{array}{llllllll}{79} & {71} & {78} & {87} & {69} & {50} & {63} & {51} \\ {60} & {46} & {65} & {65} & {56} & {88} & {94} & {56} \\ {74} & {63} & {87} & {62} & {84} & {76} & {82} & {67} \\ {59} & {66} & {57} & {81} & {93} & {93} & {54} & {88} \\ {55} & {69} & {78} & {63} & {63} & {48} & {89} & {81} \\ {98} & {42} & {91} & {66} & {60} & {70} & {64} & {70} \\ {61} & {75} & {82} & {65} & {68} & {39} & {77} & {81} \\ {67} & {62} & {73} & {49} & {51} & {76} & {94} & {54} \\ {83} & {71} & {94} & {45} & {73} & {95} & {72} & {66} \\ {71} & {77} & {48} & {51} & {54} & {57} & {69} & {87}\end{array}$

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Video Transcript

this question gives us a huge set of data and asks us first to group them into ranges. The range is that it gives start are of length 10 and start with 30. So we'll have 30 to 39 40 to 49 so on and asks us to make seven of them all the way up to 90 to 99. Now, the way that I'm gonna do this is I'm going to take each range and then run through the whole table of data points and pluck out the ones that are inside the range. So for 30 to 39 I'm gonna look over the whole data table, and I will find just the one point the 39 that's in there. So and then for 43 49 only the same thing. I'll find a 46 of 48 a 42 49 45 and a 48. Now I have Before I started this, done this whole thing and group them into groups like this. This is the method that you'll use. Um, it's not gonna be very exciting for you to watch me do this whole thing. Um but this is how you'll do it. Um, I will show the next part Part B ask you to make a frequency table. Now in a frequency table. You have one column of ranges. These are gonna be the range is that we just just came up with, right? 30 to 39. We said 40 to 49 50 to 59 60 to 69 72 79 80 to 89. And, of course, 90 to 99. The other column is going to be the frequencies. That is how many data points fell into each range. So the first really remember we only had one in the 2nd 40 to 49 we had six data points. Um, I found in the 50 to 59 range 13 data points in the 60 to 69 range. 22 72 79. I found 17. 88 89. I found 13 in 92 99 I found. Eat. Now, part C wants us to make a hist a gram of all of this history. Graham, I'm gonna draw my axes here. And to do this, we're gonna need to divide up our uh, X axis into bins. Now, the way I'm gonna do this is I'm gonna have my bins includes the left endpoint. So if this is 30 and this is 40 then the bar here will represent 30 to 39 including 30 but not including 40. And I'm actually going to make this a little bit closer so I can fit everything in here. This will be 40. This will be 50 60 70 80 90 and 100. So now that we have our bins, we also need to scale our X X is I'm gonna go by fours. Olive Teoh 24. Because I think that 22 is our maxes before eight, 12 16 20 24. And this is a hand drawn graphs. Of course, it's not gonna be perfect, but let's start plotting in the 30 to 39 range. Well, I have one. So that'll come up to here in the 40 to 49 range. Reitz six. That'll come up to here 50 to 59 was 13. That'll be right about there. Not perfect, but almost 60 to 69 was 22. So way up here between 20 and 24. Oops. 72. 79 was 17. Right about there. Yeah, 88 89 was 13. So again is gonna be there Ish in 1999 was eight. So exactly there. So this is what your history and will look like. You can see that. Um, it's pretty, uh, you know, model and symmetrical. Then it asks us to make a frequency polygon. A frequency polygon is made by connecting all the mid points of the bars on the history. Graham, Um, it's just a different way to represent a distribution. And you will, uh, admit points of the bars that you would think would be on either side. So the 20 to 29 the 100 to 1 or nine you'll have those mid points at the X axis, and then you connect them to make this sort of polygon shape. In this shape is that description of the data itself choose the shape of the data. So this is, um Yeah, this is your final answer. Your history, Graham, with a frequency polygon overlay