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Pis 66 66 9L 86 FRRAEE lelelels 80 80 08 80 85Complete the frequency distribution for the data.Height [60,65)Frequency[65,70)[70,75)[75,80)[80,85)[85,90)...

Question

Pis 66 66 9L 86 FRRAEE lelelels 80 80 08 80 85Complete the frequency distribution for the data.Height [60,65)Frequency[65,70)[70,75)[75,80)[80,85)[85,90)

pis 66 66 9L 86 FRRAEE lelelels 80 80 08 80 85 Complete the frequency distribution for the data. Height [60,65) Frequency [65,70) [70,75) [75,80) [80,85) [85,90)



Answers

From the frequency distribution, determine the total number of data. $$\begin{array}{c|c} \hline \text { Class Intervals } & \text { Frequency } \\ \hline 1-50 & 29 \\ \hline 51-100 & 12 \\ \hline 101-150 & 6 \\ \hline 151-200 & 22 \\ \hline 201-250 & 56 \\ \hline 251-300 & 60 \\ \hline \end{array}$$

Vincey table. So we need to figure out, um, how many of these scores or items were going to fall within the once in a deviation. So in order to figure that out, we have to kind of draw ourselves or think of ourselves of a number line right down the middle is going to be our mean the center. And that's going to 75.4. And then if I were to go one standard deviation, uh, and one center deviation down, that's a matter of adding the 7.7 to adding the 7.7 to that and subtracting a 7.7. So we're gonna do 75.4 plus 7.7. That gets me 83 point one. And if we do 75.4, minus 7.7, that gets me 67.7. So if you recall there were 25 of these items and so we're just trying to figure out how many out of the 70 hurt out of 25 will be within that once an innovation. So it's the range between 67.7 and 83.1, so basically we can't count the nineties. We can't count the advice. We can count the eighties. So there were three eighties plus the 7 85 that's 10 so far and then the six seventies, because we can't get so they're 16 out of 25 and a set percentage. So you'll do 16 divided by 25 move your decimal place. That's gonna be 64 percent.

So for this question, were pretty much asked to determine the total number of data. So for this, all we really are gonna look at is the frequency portion, because the frequency portion pretty much tells us the number of times you know, certain value or the values in a class interval occur. So all we really have to do is just add up all the frequencies together because that basically tells us how many times, you know, um, the data shows. So what we're gonna do is go ahead and just add everything that's gonna be 14 less 18 plus 24 plus 10 plus six. Right? So we know that 24 plus six that's gonna equal 30 30 plus tennis 40. So we have 40 plus 14 plus 18 remember, 14 plus 18 right? That's a secret into 32. So that becomes 30 to plus 40 which is equal to 72. So the total number of data is going to be sending

So for this problem and a few others after this problem, you're going to be needing to look at that frequency table. So frequency means how many times it occurs. So that means there were three different nineties. There were 2 85 3 eighties and so on. And so if we're asked to find the variance Nissinen deviation of these values, we're gonna have to still find the mean first. So if there were 3 to 376 and four that those are the numbers we need to add up to make up our denominator. So we're gonna add up Three plus two plus three plus seven plus six plus four. That's 25. So there were 25 total tests of people or whatever the situation was from the problem. Okay, so now we're ready to add up all its members. Now, the easy way to do this is to kind of think of it like this If there's 3 19 3 times 90 plus two times 85 plus three times 80 and I can help save you some time. And you calculated from adding up all of those numbers so three times 90 plus two times 85 plus three times 80 plus seven times 75 plus six times 70 plus four times 65 gets us 18 baby five. I am ready to divide that by 25 70. Look, 75.4. Okay, So in order to get the variants, we're gonna have to use all of the all three nineties have to be subtracted from the 75.4 and squared. Um, but here's thing. If you go and do that calculation for one of these for each of these, then and then square it, you would basically be ableto then multiply by three multiplied by two and so on. So you're not necessarily repeating at all these steps in your calculator if you can keep track it like that. So we're going to keep going with that same momentum. So Step two is going to be fighting the variance. So what I'm gonna dio is I'm gonna do one of each. I'm gonna dio 90 minus 75.4 and then remember, we're still squaring to get when we do our variants. But then when we're done with that week in times that by three and use that as part of our final answer in the end or final steps of 90 minus 75.4 and then we square it and we get 213 point 16 So that means there's gonna be another to 13 points 16 and yet another two. 13.16 All right, so now the nineties or done Now move on to the 85. So we have a five minus 70 five point for and then square. So 85 minus 75 point or and then squared is 92 0.16. And since there were two of those were going to start another 92.16 down. Now there were three eighties, so we're gonna dio 80 minus 75.4 Army Square A T minus 75.4 squared is 21 0.16. And so there were three of those. So another way to think of that is to just times that by three. But Sri kid do that now or later. There's not really a huge deal or difference, So I'm gonna just do that Now we got 63 point for eight. So later on, we're gonna have to be adding up all the numbers of Catholic it most at surgery 80.48 later and old kind of have to go for 17 many ways to their seven of those That be a lot of writing that we don't stealing you to dio the 75 minus 75.4 squared. So, you know, high by 75.4 is 0.4 square yet 0.16. So since they were setting of those, we're gonna times 0.16 times seven and we get 1.1 to So we'll use that number later when you need it there. Six seventies. So we're gonna dio 70 minus 75.4. I am very square that they're 70 minus 70 car point for squared. It's us 29 0.16 And because there were six seventies, we're gonna have to multiply this by six 1 74 0.96 Last one is 65 therefore of those, So we're gonna dio 65 minus 75.4 squared and that's 108 books 0.16 times four gets us 4 32 0.64 So recall that variance is all adding it all the times that we just calculated and taking the average of it. So we're going to need to do to 13 plus 2 13 plus 2 13 plus. It was to 13.16 to 13.16 plus 2 13.16 plus 2 13.16 plus 92.16 plus 92 0.16 plus. Now we already did this math. So we want the 63.48 getting at it since very did that. So just be careful that you don't over over do that. So then 63.48 plus the 1.12 plus the 1 74.96 plus the 4 32.64 So we end up getting our variance is going to be 14 90 six, divided by the number that was in the list. So we determined earlier that the number the list was 25. So divide by 25 when you get 59 0.84 Exactly, actually, so we don't need the swiftly equals approximation its attacks equal. And then the square root of 59.84 will get us our standard deviation. So senior aviation is gonna be about seven point seven or 7.74

In order to create a frequency distribution with seven equal class is the first thing we'll need to do is find the width of each class. To do this, we'll start by finding the maximum and the minimum and our data set. If you look through, you'll see that the largest number is 93 and the smallest number is 48. Now, the reason we need these numbers is to find our range, which is just the difference between the maximum and minimum that will give us 93 minus 48 which equals 45. So this basically means that our data spent a gap of 45 numbers going from 48 to 93. And to split this into seven equal classes will just divide by seven. This will give us about 6.4. And even though this normally would round down to six, we're going to round this up to seven. Because if we only use six for our with, we are not actually going to make it up to 93. So you always want to around Ah, when you're finding the wits. All right, so to start off this chart, we can start with any number between 45 48 in order to still make it to 93. I'll go ahead and start with 45 but it does not matter which number you pick. If you're not ever sure which number you should start with. You can always start with the minimum, and it'll always work out that way. Now to find our limits for each class, we need to include seven numbers because we have a width of seven. So for this first class in orderto have seven numbers, we would have 45 46 47 48 49 50 and 51. So our endpoint will be 51 which means that our next class will start at 52. Now there's a much easier way to find these numbers. You'll notice that the first class and second class start out seven apart from each other, so we can just add seven to each starting point to get our next starting point. So we'll get 59 66 73 80 87 and I would include 94 but we're going to stop it. Seven classes here, but I'll go ahead and write the 94 just to help us later. Now, to get the endpoints, we can just subtract one from the next starting point. So 59 is our starting point there. That'll mean that we ended the second class at 58 and then the 65 will end before this 66 than 72 79 86. And finally 93. I'll go ahead and erase this 94 since we don't need it. And finally, to find our frequencies will go back into the chart and count how many numbers there are between 45 51 for the first class and basically just see how many numbers are in each class. The first class only has one number in the chart, which is 48 are minimum. Then we have two went speeds between 52 58 seven for the third class, 13 12 to and three. Now you may have done a different chart from me and still gotten the correct answer. There's more than one correct answer for this. You could have started like I said before, with either 45 46 47 or 48 and depending on which one you started with, you will get a different frequency over here on the right for each class, for example, since 53 is one of the numbers and the chart. That means that if you had started with 48 the 50 threes would have been included here in the first class, so your first frequency might have been three or four instead of one. However, as long as your classes are seven and with and you start between 45 48 then your answer will still be correct.


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