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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.

Use six intervals, starting with 0–24.

$\begin{array}{rrrrrr}{7} & {105} & {116} & {73} & {129} & {26} \\ {29} & {44} & {126} & {82} & {56} & {137} \\ {43} & {73} & {65} & {141} & {79} & {74} \\ {121} & {12} & {46} & {37} & {85} & {82} \\ {2} & {99} & {85} & {95} & {90} & {38} \\ {86} & {147} & {32} & {84} & {13} & {100}\end{array}$

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Multivariable Optimization

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this question gives you a big table of 36 numbers, and at first it asks you to group them. The group said it wants are looked like this 0 to 24 and they want six of them. So it'll go. The next one will be 25 2 49 then 50 to 74. 75 to 99 100 to 1 24 and 1 25 to 1 49 Those will be our six groups or bins. Um, and what we're gonna do is we're just going, I'm just going to go through the table. And if I see a number in that been, I will put it where it needs to be. So start with 03 24 and I've actually already done this. I've got this right now, so I'm gonna go through kind of fast. But this is the general idea. As we go through, we see that we have a seven that's in that range. Then we'll get a 12 further down. We get it too. And a 13 now for 25 to 49 will do the same. Exact thing will go through. We have Ah 26 29 44 43 Um, 46 37 38 32. Next we do the next been 53 74. We get 73 uh, 56 73 again 65 and 74. Just moving right along with the next bin will get 82 79 85. You need to 99 85 95 90 86 a four and we won't count 100. 100 will go in the next. Been. So we'll start. Um, we'll start from the top looking down. We'll get one of five, 1 16 1 21 and 100 and finally will get all the numbers that are between 1 25 149 inclusive on. And that's just gonna be the rest. The ones that we haven't cabinets will have 1 29 1 26 1 37 1 41 and finally won 47. All right, so now it wants us to make ah frequency table so we can get ready to make a history. Graham, out of all of this, all of these data. Um, so let's start with a frequency table within a frequency table. We have, um I column for the range and then a column for frequency, which orchestrated f. Now we're going to use the Rangers that we just did will do 0 to 24. Um, and I'm just gonna right the the left endpoint. So 25 50 75 100 and 1 25 So those are our ranges, or at least the left endpoints of them. And then we have our frequencies. So in the first been, we had four in the second. There were, if we can come up, that are eight. Then we had five, 10 four, and in our last been we had five. So those are our, um, frequencies. And now we have this table and arranges We can build a hist a gram Soendral myself, some axes, a bill. This will be the Y axis. What? The x x is down here now in a history on the X axis has theme bins or the ranges, and I'm going to set this upset. Each been includes the left endpoint. So have zero here. And the, uh, the bin that goes here will include zero. So then I'll include the next in point that we 25 and 50 then 75 100 and 1 25 Um, and then for my y axis. I think I'm gonna want it to go up to 10. And I'll do that by twos. So we'll have. I think this will work. 2468 10. And, uh, let me do a little bit more to scale of to for six feet again. Nichols, Enough is a hand drawn graviton 100. Perfect, but it'll it needs to show what we're trying to show. So now we plug each frequency according to its been. So we know that this been the zero to 24 been had four. So we're gonna have a plot up here. The bar goes up to four. The next one had at frequency of eight. So that a go all the way up to eight. The next head of frequency of five to be there, the 75 to 175 to 99. Ban had a frequency of tens that go all the way to the top of our Why axis here. And the next one had a frequency. Ah, four. Remember the 100 to 1 24 had frequency four and their final being had a frequency of five like that. And just for clarity's sake, I'm gonna I'm gonna label these. We're gonna have four. Eat five, uh, 10 four and five. Now, the last part of this question wants us to draw frequency. Polygon and African polygon is basically all you're doing is you're connecting them tops of the midpoint of the tops of each bar in our history. Graham, um, it's just a different way of sort of showing the same thing. Um, so let's do that when you're doing a free concert pavilion where it's not always clear where to start on the left or finish on the right, Um, when you're on the left, it is a good idea just to start at the midpoint of the bar. So since this bars goes up to four, all started to men will go up there connects the four to the eight. It's not again. Don't have to be perfect, but we should to strive for some clarity. From 4 to 88 down to 55 up to 10 10 down to four, and for over 25 and connect this to the mid point of 502 and 1/2 fish. And that's Ah, that's our frequency Polygon. It looks something like that. And ah, so this is what your final answer is gonna look like.