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Homework: Unit 2 Homework Score: 0 of 4 pts 2.5.11Use the accompanying data set to complete the following actions Find the quartiles b. Find the interquartile range...

Question

Homework: Unit 2 Homework Score: 0 of 4 pts 2.5.11Use the accompanying data set to complete the following actions Find the quartiles b. Find the interquartile range Identify any oulliers63 63 56 5758 61 57 61 54 55 62 61 64 77 D Find ihe quartilesThe first quartile, 0, = The second quartile; 0z, Is | The third quartile; Qz. Is E (Type integers or decimals )

Homework: Unit 2 Homework Score: 0 of 4 pts 2.5.11 Use the accompanying data set to complete the following actions Find the quartiles b. Find the interquartile range Identify any oulliers 63 63 56 57 58 61 57 61 54 55 62 61 64 77 D Find ihe quartiles The first quartile, 0, = The second quartile; 0z, Is | The third quartile; Qz. Is E (Type integers or decimals )



Answers

Finding Quartiles (a) find the quartiles, (b) find the interquartile range, and (c) identify any outliers. $$\begin{array}{llllllllll} 42 & 53 & 36 & 28 & 26 & 41 & 37 & 40 & 48 & 45 \\ 19 & 38 & 36 & 56 & 43 & 34 & 52 & 38 & 50 & 43 \end{array}$$

So hear me. Eso data data. So to find the value off que two, we will look at that my daughter value. So there are 15 total values. So here, ISS you too. So computer easy 40 34. Then you will find 21 So here you can see that in this part of the data set, nominal value is 25. So when we Q one So Q one is 25 chairman early. This part of the data said the middle very is okay, is having it's pretty weak. U t So it's easy for 2. 47. Next, we will find inter quartile range. Just quite a few team, I ask you one still you're 22. Next we will find for out liars. You have to find the value to one minus 1.5 times off and I t rod until week. We're to 25 minus 1.5 22 and he could do minus eight second. Really, we have to find its guilty plus 1.5 times off Kivar on will be 2047 last 155 22. Way to keep this. So here we can see that data said. There is no value, which is stand minus eight. All are greater than 80 so there are no other players.

In this question, you're given a set of 20 data values and asked to find the portals, the inter quartile range and to test for any outliers. The first step in any question like this is to sort the data in order from least to greatest, which is always a little bit tedious. I've chosen to put my efforts into typing the data into a spreadsheet application, and then I used a command called Sort Range, which is usually found under a data menu to have the computer put them in order for me. So make sure I'm not missing anything. And for your sake, I've also added a set of numbers so we can tell which data point we are discussing. Remember, the core titles are going to break the data step set up into equal fourths. It's often easiest to find the second quartile first, which we've been doing for years, also called the median. So that's exactly halfway between my data. But that would actually fall between two numbers so you'll average those two numbers divided by how many which will give you 22.5 as your second quartile or your medium. Then, looking at each half of the data. Let's look at the first half of the data again. Halfway through those 10 values will be right between the fifth and the sixth Data point. That gives you a first quartile equally 21. Since both numbers happen to be the same, and in the bottom half or the second half, you'll go down there between the 15th and the 16th data. Those are the same values, so Q three is 24. Remember that your inter quartile range means the difference between the 3rd and 1st quartile, so your I Q R. In this question is 24 minus 21 or three. The next big thing to really note down is that you need to memorize for this section is that you need in order to test for outliers, you want to calculate 1.5 times your I Q R. So that's 1.5 times three in this problem, which gives me 4.5 as this value I'm going to use to find the boundaries to check for outliers. So what you do with that value is you extend away from the middle, um, past your portal out of court. So we'll do 21. It will subtract 4.5 to get a number lower than 21 will get 16.5 as my boundary check for out letters insist that number is lower than any of my data. I have no outliers at the lower end. At the other end, I'm gonna extend this value farther away from the medium. So in this case, I'll add 4.5. Give me a value of 28.5 as a boundary to check for quarter to to check her out letters. Excuse me. So that would fall right here after the 25 before the 29. Which means that the 29 is farther away than that boundary. So it's considered an outlier. And that's the last of all that they asked in this problem. Oh,

So here we have sorted out on the 15 venues, and then you does it. So the median would be the middle value off the sort of data set the median, which is also called do you to 60. Here, you can see that. 1234567 seven venues here. 1234567 seven Values and did side. And this is cute. So for the first quarter tied would be the media after data will use below Q two. So it will be for this portion. This is a first quarter type. So the middle value, uh, for this section would be 21 and kill me. 57? Yeah. Likewise, Q three will be with the really from this section. Um, that that you will be okay. 63. Okay. Next, we're going to find out inter quartile range. So putting the values, we should get six now to identify our fire out liars, we have to find out to values Q one minus 1.5. Thank you are and killed three plus 1.5 off like you are. So it will be 50 salmon minus 1.5 times six and 63 Goodness, 1.5 by himself. Six. This very will be 48 this value will be 72. So anything below 40 it would be out lied and anything about 70 to be an out liar. So here we can see that we have a value, which is about 72. But we have no value. We just below 40 years so you can see that 80 years an outlier. Come on. So we have our answers here. Q one is 57 median poor second quarter Silas 60 third quarter minus 63 Book I Q. R. S six and we have gotten our flyer, which is 80.

Hi everyone in this video we're going to use a five number summary and a box plot to look at the statistics of 21 patients first, make sure to sort all your data from lowest to highest. From 1 to 55. Next we'll find the median or the middle number because we have 21 patients or 21 observations. We'll look for the 11th patient 123456789 10 11. So this seven represents our median write that down. Q. Two. Mhm. Mhm. Q two are medium is seven X. We'll find quartile one which is half of the first half. So make sure to include the median when you're counting for the first half. So we have 10 on the left side plus the media. So we actually have 11 observations. So the middle of 11 is six. The sixth position or the sixth patient 123456 So the second floor represents cartel one. Mhm. Next defying quartile three with the same thing but also keep in mind to include the median. So 123456 Yeah. Yeah this 12 will represent quartile three. Ex interpret this courthouse. We can treat each section of our observation, this one section, another section, third section and fourth section we can treat each section as 25% of our data. So for example all the patients have stayed from 1 to 4 days represent 25% number data patients that state from one day all the way to seven days represents 50 50% of our data. Likewise, quarter to three patients have stayed from 1 to 12 days represent 75% of our data. Next we'll move on to inter quartile range. Now from the formula quartile 3 12 minus Corta 14 is eight. One second. This 12 this eight represents um The range that contain 50% of the data. If we were to look at patients have saved from four days to 12 days you see the difference is eight. So within the eight day timeframe we have 50% of our data. Next we move on the part C which is the five number summary. Our minimum number one our court to one four. Our median seven without 3 12. And our max 55. The reason people see next you move on two. The lower and upper limits starting with lower limit will be 4 to 1 which is four minus 1.5 right lower limits equals to four minus 1.5 times. Are inter quartile range of eight which is negative eight. For upper limit you have cartels 3 12 plus 1.5 I'm eight which is 24. Now let's start by interpreting the lower limit first of negative eight. That means patients to have stayed um at the hospital for negative eight days, which doesn't make sense because you can only stay a minimum of one or none. Um So we can disregard the lower limit because no patient will stay for negative eight days. However, for the upper limit we have 24 so a patient have stayed for more than 24 days will be considered an outlier. If we were to look at our data, we do have one observation above 24. We have one patient that stayed for 55 days that will be considered are outliers. Next we can visualize the outliers and our courthouse using a box plot. Please give me one moment to draw the box plot. Here's the box plot. As you can see we do have a red cross at 55. This represents our outlier. the one patient have stayed for 55 days, whereas the rest of the our data of our 20 patients are within a one 2 23 range. So we have 23 as the maximum because we do not count the outlier as the right most whisker for the rest of the box plot, we have. The blue line. First blue line on the left represents quartile one red line is our median second blue line or the right most blue line represents quartile three.


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