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Question 57 (8 points) Name and explain everything wrong with the following grouped frequency distribution table:X 12-21 0 21-30 3 30-39 39-48 ; 48-57 57-68 2 75-84...

Question

Question 57 (8 points) Name and explain everything wrong with the following grouped frequency distribution table:X 12-21 0 21-30 3 30-39 39-48 ; 48-57 57-68 2 75-84 1 84-93 2 93-102 2% 0 15 15 2 20 0 0 35 35 .1 10 05 5 10 1 10

Question 57 (8 points) Name and explain everything wrong with the following grouped frequency distribution table: X 12-21 0 21-30 3 30-39 39-48 ; 48-57 57-68 2 75-84 1 84-93 2 93-102 2 % 0 15 15 2 20 0 0 35 35 .1 10 05 5 10 1 10



Answers

Construct the histograms and answer the given questions. Use the frequency distribution from Exercise 15 in Section $2-1$ on page 49 to construct a histogram. Does the histogram appear to be skewed? If so, identify the type of skewness.

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.

So in the given question we are told to find the missing frequency. Indeed given distribution. Right? So the distribution has given us we have eggs and F. The value of X. Has given us 246 And aid. And the corresponding value of F. Which is the frequency is 35 six and white. So we need to find the value of the missing frequency. Why we are given that the mean is equal to 5.5. Right? So the mean is taken by immune is taken as the sigma of F times eggs divided by sigma of earth. Right? And this is equal to 5.5. So now sigma of fx is two times three plus four times five plus six times six plus eight times wide. They were and by sigma F is three plus five plus six which is eight plus six. That is 14 14 plus Y. Is equal to 5.5. So when we multiply 14 plus Y with 5.5 what we would get is 14 times 5.5. S 77. So 77 bless 5.5 White as equal do six plus 20 plus 36 is equal to 62 62 plus eight one. And from this weekend, right, eight White minus 5.5. White is 2.5. Wife is equal to 77 minus 62 which is 15. So why? As it will do 15 divided by 2.5, which is equal to the which is equal to six, Right? 15, divided by 2.5 is equal to six. So the missing frequency of the given distribution. The six. I hope you understood the method. Thank you.

When we count them for zero one to three and four I'm gonna put the frequency in blue We count 24 zeroes 16 once, two twos, two threes and 14 making a total Which I wanna put in blue 45 Yeah. Now when we graph it as a history Graham, it is going toe Look, something like this. Now from this hissed a gram When you graph it yourself, there is a strong positive school nous appeared because the highest peak bar this fund is existed in the left and increasing to the right.

Hell in this problem we have to find main invariance by using the given data. So here we have given the following table. First of all, we will find the mid values that is X I. So we get five 15, 25 35 and 45. Let assumed mean as equals two 25. So in order to find the mean, first of all, we will find you Y which is equal to X I minus assumed mean Upon 10. So we get EYS minus two minus one 01 two. Now we will find a fi you Y it would be five into -2 is -10 18 to -1 is -8, 15 in 2, 0 is zero 16 into one is 16 and six into 2 is 12. Similarly, we will find similarly, we will find a fire you a square. So we get 20 seat zero 16 and 24. The submission of F i U I is then and The submission of FIUS Square is 68. Now we know that Mean as equals two assumed mean plus sigma, F I U Y. Upon submission of F I into age here edges the height of the class interval by substituting the known will use we get Mean as equals two 25 plus 10 appoints stay into 10 by simplifying it. We get 25 Plus two which is equals to 27. Now we will find variance. We know that variances equals two hide square a bone and square and do and into sigma. F I U I square minus sigma. F I U Y who square by substituting the known will use we get penn square are born 50 square into 15: 68 -10 sq. By simplifying it. We get 100 upon 2500 Into 30 400 0. It would be equals two. Run upon 25 into 3300, Which is equals two, 132. Hence we get me as equals two. Mhm. 27 variances equals two 132.


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