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PARTThe following table shows a sample of the amount Sp ungrouped data: It is the same data used that this is Assignment; so you can save time by referring to you e...

Question

PARTThe following table shows a sample of the amount Sp ungrouped data: It is the same data used that this is Assignment; so you can save time by referring to you extra columns are to help you organize your work_ column. Provide your own headers for the col coervASWen Filling in this table is optional. It is your worksheet ifyou want Lunch Spending S) Z-scores 28 1015101. What is the range for this sample?

PART The following table shows a sample of the amount Sp ungrouped data: It is the same data used that this is Assignment; so you can save time by referring to you extra columns are to help you organize your work_ column. Provide your own headers for the col coervASWen Filling in this table is optional. It is your worksheet ifyou want Lunch Spending S) Z-scores 28 10 15 10 1. What is the range for this sample?



Answers

Find the standard deviation of sample data summarized in a frequency distribution table by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3­4 with the original list of data values: (Exercise 37) 11.1 years; (Exercise 38) 9.0 years; (Exercise 39) 13.4; (Exercise 40) 9.7 years. (TABLE CAN'T COPY)

So once again we're giving a frequency table that has classes, and what we need to do is figure out what the mid points are for those classes. So we can figure out what the standard deviation is already given a frequency. And uh if we multiply that frequency by X, I'm just going to be our midpoint, we'll be able to calculate our standard deviation. So, for example, we have our first class at 20-29, Which is a class with nine or 10, and the mid point for that, simply going to be the average of the tomb. So 20 plus, 29 divided by two, Is it going to get us 24.5? And if we let the midpoint b x, we'll get a better uh approximation of what the standard deviation is, and then we'll just take our frequency there. So, what this is gonna look like is our standard deviation is going to be the square roots? Yes, it needs to be this big and we'll take our sample size, which is simply going to be the sum of all the frequencies, So that's going to be 38 plus that, plus that. Okay, so 82. Yeah. And then we will multiply that by the some of the frequencies times the midpoint squared. So we're gonna have a frequency of one for our first one times 24.5 squared. And then we're gonna add on the other 81 values. This is best to be done in Excel, I've shown in a few other videos how to do repeated calculations. So we'll do that. Close the parentheses E for that first one and then we'll get to subtracting the sum of everything squared. So what that's gonna be is we're gonna subtract one times 24 five and we are going to square that. Yeah. And added to all the other ones. So that's gonna be another open parentheses there. And then we'll divide that by our sample size of 82 and multiply that by one. Less than the sample size. Yeah. And that will be our standard deviation. And what we will see is that the standard deviation comes out to be is 9.69 years.

All right, so the standard deviation is going to be modified a little from our frequency table formula, we're just gonna be multiplying the frequencies times the mid points, which will call X. So what this is going to look like is uh following we're gonna take the square root of our sample size, multiply that by a couple of different sons. So our sample size is 121, And we'll divide that by 121. I was 1 -120. 120. I'm gonna go ahead and move this down a little. Just like, can get myself a little bit more room, we're gonna draw in the rest. So that's gonna be the some of the frequencies times the X squared. So we're gonna go ahead and calculate the first midpoint and the first frequency and leave the rest up to you guys. So that's gonna be 50-59 for our first category. Uh so that's going to mean that our midpoint is going to be between the two, and that will be 50-plus 59 Divided by two. And that's gonna get us a midpoint of 54.5. Yeah, well, multiply that by our frequency and that will be our f times X. So for this one It's going to be 54, 5 Times It's A Frequency four. Mhm. And give the mind that this parts that X. Is going to be squared school square, that midpoint and at a whole other bunch of them. Uh because there's 121 of them. so that's gonna be a couple more to do. It's actually just gonna be seven of them, There's seven categories to do, and then you're gonna subtract that from the sum of everything squared, So what's that can look like is 54.5 times four, and this is going to be squared it, and then you're just going to add the other seven that are left in that formula. Yeah, and that is going to be the general form of our standard deviation. What it comes out to be is going to be 13 47. Yeah, and I don't think we have any units actually, we might We don't but we can compare this to exercise 39 with an standard deviation, that was 13.4 mm. And to be off just by .7 is actually pretty close

So we're gonna be calculating the mid points um to find out what our standard deviations are for our frequency class table. To find out the standard deviation. We're going to apply this formula and just add these frequencies and read to our fast way of calculating standard deviation. So the exes are going to be the mid points and mid points are going to be found by adding or two and dividing by two. So for our first class, the mid points can be too, For the second class the midpoint will be seven and so on. What we can do is calculate the first two and leave the rest up to the math. So this is going to be, the standard deviation is given by Our sample size of the some of the frequencies, which is going to be 33 and then we'll multiply that by the some of the product between the frequency and our midpoint squared. So that's gonna be for our first one, eight times 2 squared plus the next one, which is going to be two times seven squared. And we'll keep on going for the other uh six classes and then we'll subtract that from the same things here, but they're not gonna be squared, so it's gonna it's gonna be eight times two plus two times seven. And the rest. And this is going to be squared, This is all gonna be divided by within the square roots, By the sample size of 33 times one minus a sample size. Okay, And then this is going to result in a standard deviation of 9.84 years mm.

In this problem, we have to find the mean. I understand that the aviation for thinking one group dick up the Yankee one in Dulles allowed gift frequencies to find the mean and standard deviation. Be required some more columns off X X squared and affects and effects square our excessive midpoint off the double, which can be found as the biggest 39 divided by two. So for fasting, double our X is that before going five x square that this square before 0.5 is bourbon 90 point to find the frequent thank you want is bun, so effects will be. But people like my 34.5 visit will do that before four and five, and a fixed squared will be what multiplied by 11 19.25 So but by 90.25 now. Similarly, we will find all these values for the Double 40 to 49 x, That is midpoint is it will do for people is 49. Divided by two. Mitch is equal to 44.5 x squared that this square 44.5 is 19 eg 0.25 now effect that this six might be playing my foot before blind faith is to 67 and a sex squarest six months deployed by bun time eg 0.25 So this is equal do but one a take one. Why fight in the same thing? We've been fined or X values for all the Cuban in the bus. Well, in this day we have completed our fifth day. But we also found the system off all the sequences that this information if and also summation effects and summation f X squared Now to find this time that aviation be the first fine Do you mean and is equal to summation f which we have found to be going toe 80. As we noted, form lover me expand is summation effects divided by em. So no mention FX we have found is it will do 5550 divided by n that this divided by 80. So however me x but is equal to 69 point to the it our mean Is he going to 69.38 Now we will use the formula for standard deviation to find standard deviation. The farm number stand the aviation s is another good summation at fixed. Squared minus. Hey, it's bus. Good. Do you mind? Made by n minus when some mention affects quit. We have found to be 1 to 401 x 30 minus. And he will do if he my dad liked by express scripts were expands Our me between found Toby Puerto 69 point to the A We have the tickets square. Do I gain by any minus one? Our anything will do. MP, So n minus one is a T minus. Work that this 79 so divided. Advice 79. Now this is it will do for being blind. 56 So our required answer that this standard deviation is equal do for 10.56


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