stem-leaf-5-qquad-7-7-7-8-9-6-qquad-3-4-5-5-6-7-7-qquad-2-3-4-5-6-qquad-6-3-63

Question

Stem Leaf
5 $\qquad$  7 7 7 8 9
6 $\qquad$ 3 4 5 5 6 7
7 $\qquad$ 2 3 4 5 6 $\qquad$ 6 \ 3 = 63

Trinity Steen · Accepted Answer

All right. So remember, 13 were asked to find the standard deviation, but Nor to find the center deviation, we&#x27;re gonna have to calculate the variance. And we need mean the average of our list given in order to do any of that. So first of where to were given a stem and leaf plot. And, um, it&#x27;s just there to kind of have everything be there for you. Organized in order from smallest to largest. But you&#x27;re gonna have to rewrite everything out. Um, set where you can kind of have everything listed out, um, to be able to find the meat. So first things first, you define the mean of the of the list. And so that&#x27;s when you add up all the numbers and then you divide by, however, much is in the list. So we&#x27;re going to do that real quick by adding it. 57 last 57 plus 57 plus with the eight plus 59 plus 63 64 plus 65 65 66 67 plus 7 2% agree with 4 75 76 So there I get a total of 1000 48 there were 16 numbers in the list. So our X bar, which means means or average, is going to end up being 65.5. So that&#x27;s exactly 65.5. And so now we&#x27;re gonna be test with is using that mean to calculate the variants? So you&#x27;re going to take all the numbers in your list and they&#x27;re going, though basically, rewrite them all out in a steptoe, find the variance So it&#x27;s It&#x27;s a little bit easier if you kind of follow a method. So eventually you&#x27;re gonna be subtracting your list items minus your average as a new square. That&#x27;s that way. You can always end up with positives. So, um, just for sake of keeping things orderly, I&#x27;m going to rewrite the the items out from the list, and then everything is gonna be getting sidetracked by 65.5. So for the sake of time I write down like that, there&#x27;s an air of there, and I&#x27;m gonna put parentheses around these because that shows that we&#x27;re gonna do subtraction first, According Toa, please excuse My dear Aunt Sally, a pen dos lord of operations. Whichever way you call it all right. And then we got to keep going with the rest of the list. So we&#x27;ve got a second column here, will be doing the same thing and so on. So we&#x27;ve got 60 for next have got 60 60 to 65 every 5 56 in the 67. So that&#x27;s right. The minuses. And then again, for the sake of time, going to straw narrow down that that is gonna be a repeated situation. We&#x27;re gonna square Well, that and then we had the ones in the seventies, so we had 70 to We have 73. 74 were 75 million facility sits not. And then remember, we&#x27;re attracting the average and then square. Okay, so let&#x27;s get that accomplish. Will use a dominating the text box to be ableto right in all these. Good. That&#x27;s gonna hopefully help save some of the room here cause it is a little bit space usage. Move this of over todo just for the sake of keeping things orderly. Yeah, a little bit better That way. This Colin isn&#x27;t all smushed. Okay? What if we need to cut so 57 I minus 65.5 and we&#x27;re square that and you get 72 0.25 when you skirts of 72.25 Then you&#x27;ve got 57 minus 65.5, and you square that we get a positive Oops, that&#x27;s another 57. So it&#x27;s the same. It&#x27;s the same thing. 72.25 72.25 and then our down under us up the new 58 minus 65.5. And risk where? That and we get 56 0.25 59 minus 65.5 squared gets us 42 point too far. Okay, so now we&#x27;re ready for this one 63 line of 55.5 and we square that it&#x27;s going to equal 6.25 64 months. 65.5 squared gets us equal toe to point to fuck 65. Last 65.5 is 1/2 square. The half get point 25 and that&#x27;s gonna also be a 0.25 It was the same number 66 minus 65.5 will also be 0.5 squared. So that&#x27;s another 0.25 and then 67 minus 65.5 squared there is too 0.25 Now I live. He&#x27;s over. Just just imagine so that when we know we can fit everything. Okay, so 70 to minus 65.5 and squared is gonna be 42 0.25 73 minus 65.5 squared. It&#x27;s US 56.2 five 74 minus 65.5 squared. It&#x27;s us, uh, 72 0.25 75 months. 65.5 is the important five squared is gonna guess 90.25 and our last one 76 minus 65.5 is temper. Five squared is 110.25 Okay, so we have all these numbers now that I just typed out, and those numbers need to be added up and divided out by 17. Gonna find the variation of this and the variation is the average of all those numbers that we just captain. So I need to add up 72.25 plus 72.25 plus 72.2 sides plus 56.25 most 42.25 plus 6.25 plus 2.25 was 25.5 plus 25 plus 2.25 plus 42.25 plus 26.2 five plus 7 2.25 plus 90 0.25 less 110.25 We added all those up to get 6 98 and remember there were 16 items on our list. So to 6 98 divided by 16 and you&#x27;re gonna get a pump, you&#x27;re gonna get exactly ah 43.625 in order to get the standard deviation, the standard deviation. Who&#x27;s end up being the square root of that variation that we just rounds. Of the 40 3.6 to 5 rounded to the nearest tents, it is going to be 6.6 approximately

Trinity Steen · Answer

all right. So for number 12 were given a stem only flattened, rest to calculus. Standard deviation. So pretty much we&#x27;ve been fighting the variance. And this in a deviation all this time from since number three. So we&#x27;re pretty much doing the same thing that we&#x27;ve been doing this entire time. Except now, just the final final answer is the sooner deviation. Is there any gold? Now, this is a stem and leaf plot. What you&#x27;re gonna want to be able to just go ahead and look at your suddenly pot and go ahead and take it apart and turn it into a list. Like what the other problems looked like. So I&#x27;m going to go ahead and type those out. We at 44 45 46 47 40 seven, 53 55 56 57 58 59 67 67 68 69 69 a. M. Another 60 night. Okay, it&#x27;s gonna take these numbers and it&#x27;s good. Accountable these numbers first, so we know how much divide by for our average. Just give me 123456789 10 11 12 13 14 15 16 17. The 17 numbers are in our list, So our first task is going to be to find, you mean so remember, when we find the mean, that means we add up all the numbers and provide by how many is in the list. It&#x27;s going to go ahead and do that road quick. So we&#x27;re gonna take our calculators and add up those numbers. So we&#x27;ve got 44 plus 45 plus 46 plus 47 plus 47 plus 53 past 35 plus 56 57 plus 58 59 67 or 67 or 68 the 69 for 69 plastics tonight. And so I got 976. So that 9 76 and we divide by, I believe you said it was 17. We get 57 0.4 when we round to the nearest tent. So now our task is going to be taking our 17 numbers in that list and subtracting those numbers from the 57 minus 57.4. So that&#x27;s gonna be step two, and that&#x27;s gonna be us technically finding the variance of Step two is to find the variance. So we&#x27;re going to subtract all of our numbers minus 57.4, and then we square it because some of our numbers that we get are gonna end up being, um, negatives and we don&#x27;t want negatives. So we&#x27;re gonna go ahead and start doing that subtraction that little quick and that is the most time consuming part is this variants aspect of the problem. But it&#x27;s very repetitive, at least, so that kind of helps the situation. So we&#x27;re gonna do 44 minus 57.4. We put parentheses around that square symbol on the same thing for all the other things. So 45 miles, body high, my eyes 57 more more than smokes. Well, more. I won&#x27;t 40 spoon during other, bro. No, we&#x27;ve got 50 miles. Seven four for the sake of time. When I want to go ahead and do is just right out and numbers in that list real quick. So we got 50 six, you&#x27;ve got 57 58 50 nine. You&#x27;ve got 67 and we&#x27;re more worse attracting from the saying members I&#x27;m just gonna draw narrowed down just a show that we subtracted from that same number. And then we&#x27;re still squaring. So for good measure might be good to put that there. And then, um, you still had a few more to write down. So we had another 67. We had a 68 and then we had 60 69 69 and glasses again. It&#x27;s 57.4 getting subtracted. We go all the way down here and were squaring, So Okay, just so that way we can kind of keep track of time here, and you can kind of see the pattern. Hopefully, no, it&#x27;s OK. And I were actually to go do the actual math instead of just getting all set up. So we&#x27;re gonna do 44 minus 57.4 and we&#x27;re going to square that we get 1 70 nine my typos in because they could be big 1 79.56 Forget 45 minus 57.4. And we square that we get 1 50 3.76 We get 46 minus 57.4 square that and it&#x27;s 1 29 point 96 47 minus 57.4 square that we get 108 point 16 53 minus 57.4 squared gets us 19 point 36 ready for a new text box over here. Okay. And we&#x27;ll do that. Math in that column 55 minus 27.4 squared. Get this. 5.76 56. Minus 57 point or squared gets us 1.96 57. Last 57.4 squared at this point. 16. 58 minus 57.4. It&#x27;s this 0.6 squared at this 0.36 59 months. The 7.4 squared It&#x27;s this too. 0.56 67 Linus with the 7.4 squared is 92.16 Last column 67 minus 57.4 squared gets us 92.16 Well, there you go. Okay. 68 minus 57.4 squared gets us 112 0.36 69 minus 57.4. Squared gets us 1 34 0.56 And since the other numbers air also, uh, 69 we&#x27;re gonna do the same thing, so we can just read. Type those out. We write those out as is. So what we have to do now is all the numbers that are typed up and our box of those are going actually get at it up to be come on average. And that averages called the Variation. So we&#x27;re going Teoh, find the average and that&#x27;s gonna get us or Variation. And we need the variation in order to be able to calculate the state of deviation, which is our final answers here. So we&#x27;re gonna add up all these numbers and divide by the total number in the list for 17. So we&#x27;re gonna do 1 79.56 plus 1 53.76 plus 1 29.96 last 10816 plus 19.36 plus 5.76 plus 1.96 This 0.16 plus 0.36 plus 2.56 Let&#x27;s 92.16 Last 92.16 plus 1 12.36 plus 1 34 point 56 plus 1 34.56 That&#x27;s 1 34.56 So in that total, we get 13. 01 13. 01 0.96 And we divide by 17. So we&#x27;re And divide that by 17 and we get, uh, seven. De six point six will say, And then we square root that number and that will be our standard deviation Much is about 8.8.

Mihir Nayar · Answer

everyone. Today we&#x27;re solving problem number 22 from chapter two of the text, which asks us to construct a stem. And so I&#x27;m just gonna write down some both. So obviously, this is a new type of What&#x27;s that we&#x27;re learning about Anybody there about that, but and Mr Graham&#x27;s as ways to represent Oh, a Some of the least represent, I should say, Oh, wanted to debate up. Um, and stem Aly bots are just another way to do that as well. Again, it&#x27;s another way for quantitative data. Some of the write that down want to tiu and remember quantitative data is is data that is, murder includes numerical values. They represent how much or how many of salt. It&#x27;s a quantitative in nature. Um, there&#x27;s always gonna be a vertical line, separates numbers, shocks me in a little more in detail very soon, Nicolai and something else that a super super important to include I&#x27;m especially for your greater is a key which is basically gonna be a mini version of what? One number to the left and the one number to the right of the vertical line. What that is indicative of in its numerical about. So I&#x27;m going to draw the vertical line. And I&#x27;ve been talking about for a minute Now, front of ask, draw a straight line. Something like that. Um, and in this particular problem, murder than 16 total numbers. So the leading digits of each data value will go to the left of the vertical line. And then, uh, we will record the last digit of each dina value to the right. Um, the key will be something you always must include when you draw some. We fought, and it is basically what I like to call a mini sample size of what one numerical value in your data set would represent based off of the seventies. Um, so what&#x27;s it started? So, um, I organized the 60 numbers from, uh, in a sending order from least greatest value. So 57 was my first number, and 85 was my last night. So, um, on the left side, I&#x27;m going to have to have bye for all my fifties sex leading digit six for all my sixties absolutely indigent for all sixties, um, seven on my seventies and are a eight. So again, those air you&#x27;re leading digits and then Now I&#x27;m just gonna put the numbers and I&#x27;m gonna put a comma on the right side. Just show the separation of your stuff. So 57 is one of my numbers. It&#x27;s the first number that I have. 58. That&#x27;s it for fifties. Very nice than I have in my sixties. The first number 64 and I have 65 and I have 68. Pretty simple. Now, the seventies. It gets a little more complicated in the sense that you have to write more numbers on the right side of the world. The line. Because we start with 70 then we have to 70 news. When you have repeating numbers, you just write that, uh, right digit. Sorry, that last digit. Um, again, Don&#x27;t assume that. Basically, just don&#x27;t assume that you can only write once. I mean, do you have the right to twos to show that they&#x27;re to 70 and you have 75 guy and 75 repeats twice. So right, five, twice. I have a 7 to 6 in the state, I said, And the 78 It&#x27;s a clearly lots of seventies. Uh, and then we have these, so I have 80 as one of my values to another one 83 mother one and my last and greatest in numerical value. Data point these 2 85 So, um, this is your son Lee fought. However, you&#x27;re not done. You need to write a key. Remember that. I&#x27;m gonna put a big star here because this is something that a lot of students center forget instead, including this heat. I know in AP statistics, not including you, and drying 70 pot will use you one of the four points. If it&#x27;s an 80 problem underneath, you need to prove that. Um So what I can write, for example, is that seven and let&#x27;s just choose one of ours. So, like, let&#x27;s say, 75 for instance, it&#x27;s gonna be equal to 75. That&#x27;s basically what you just want to show you read it pretty simple, But something so simple that a lot of CNN center for yet, um, one last thing. This is actually really cool. If you turn your computer screen to the side as I&#x27;m doing right now, you can actually figure out the shape when you deal with distributions of your data set. So when you turned this to decide, you can figure out that Oh, I had the majority of my numbers in my data set. Do you like the right hand? 50% versus the left hand, 2%. So that&#x27;s something pretty interesting. And when you get Maur into skewed left right, which is a little bit ahead in terms of like describing the distribution 70 pots, actually super helpful. And there you have it. If you guys enjoy the studio piece of the light, but next to it, I hope you&#x27;ll have a nice day, Thanks.

Ankit Gupta · Answer

here. V ho three Divided by five divided by six Divided by seven Visual Big was toe three divided by five. When we have two fractions to be divided, then the second fraction in denominator will get inverted and multiplied. So we have multiplied. Best seven divided by six. No. Three can cancel 62 times. Therefore, we have in numerator one multiplied by seven, divided by Indorama toe five multiplied by to which is equal toe seven divided by Penn that is over.

Heather Zimmers · Answer

we have 6/7 divided by negative 1/3 and we know that dividing by a fraction is the same as multiplying by. It&#x27;s reciprocal. So this is the same as 6/7 times. Negative three. We can call that negative three over one and then we multiply the numerator tze and we get negative 18 and we multiply the denominators and we get seven. So our answer is negative 18 7th

Katherine Mcgovern · Answer

Let&#x27;s divide 26 22 hundreds by 76. Our first step is to move the decimal point straight up. Since our divisor is larger than the number, we&#x27;re dividing it into our dividend. We&#x27;re going to have a zero in front of the decimal. 76 does not go into 26 however. 76 goes into 262 about three times 76 times three 18. Carrier 13 times seven is 21 plus one, which is 22. So we get 200 28. We must subtract. 12 minus eight is 45 minus two is three bring down or two 76 goes into 342 Probably one more time than this. So we could say 76 times for four times six is 24. Four times seven is 28 plus two is 30 so you get 304 Subtract from 342 12 minus four is eight three minus zero is three. We don&#x27;t have a zero remainder yet, so we need another zero and bring it down. So this is still larger. Uh, and actually, it&#x27;s larger than this by about 76. So it goes in five times. Five times 76 is 380. When we subtract, we get a remainder of zero. So our quotient is zero and 345,000.

Problem

The table below shows the rebounding totals for t…

Problem 13 Medium Difficulty

Stem Leaf
5 $\qquad$ 7 7 7 8 9
6 $\qquad$ 3 4 5 5 6 7
7 $\qquad$ 2 3 4 5 6 $\qquad$ 6 \ 3 = 63

Answer

$\approx 6.60$

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$\approx 6.60$

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Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, HayekAlgebra

Catherine R.

Anna Marie V.

Alayna H.

Michael J.

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Algebra