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Joseph Brian Roswell
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Histogram and IQR
Added Sep 14, 2022
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good morning good morning good morning we have been working on data unit with the interquartile range where we have Cabell a word such as median mode range mean and identify or the ability to answer questions based on the data. The lower quartile or she won as well as 23 which is the upper quartile the minimum maximum and so far now today what we're going to do is we are going to use this data set that I have written on the board to review the IQ are as well as wired to the histogram and what we have on the border right now is illustration of a histogram and I'll perform bullet points up here for us to be mindful then I put a note side and I'm going to go into great detail that and although I have created a I've labeled the taxi in this manner to illustrate that this is not a okay and why is night except when we discussed that all right or very similar in terms of looks to a bar but it is a little wider in terms of the width of the bar the bars it's all are connected to one another to each of the other range of numbers the bars represent a range and we discuss what range the vocabulary word anybody know or recall or want to share Mister Braylon what range is defined as breakthroughs needed the largest number and the smallest number and you subtract them that's how you been a difference between one set to another set that's correct okay and so therefore the Barns and represented as a range of a category and income as we discussed we are kids wearing different color shirt when you identify a kid wearing a blue shirt and a blue baby blue royal blue sky blue so all of the types of colors of Blues we're going to the same category bars if we were okay so that's why I when do the bars represent a range of a category that we want to identify the metal bars have the same intervals you look on here I did this as an error so that way you could not make the same mistake and when we talk about animals or talk about the range of the Trot away we are referring to in this example we have a range of 1 to 10 a difference of 9 then if I go to the next bar and represents a but yet the difference between those two is only 4 then I go to the third bar and I see a range between 16 to 30 40 so you can see that there's no Circle C in terms of the rain that should be there all right so this is not acceptable and this one because BC because it's does not have the same range or intervals that is sure all right that's why it's important to understand that what it is acceptable is as an example letter I'm just going to erase the bars wider so you can see what I'm looking for you to admit I can say that I want one through 10 11 20 21 through 3031 through 40 now each of the representation of the bars in the represent the same quantity of intervals each category the difference between or the rain from 10 to 1 is 9 the rain from 2011 is 9:30 21 million just so you can see that we must have it consistent okay questions on that so far are you sure all right so now why are histograms used well can you imagine that we had numbers 1 through 40 as an opportunity to bring you had randomly picking numbers from your cards and then we said oh I found a 10-7 I found that 41 and then you have a bar graph with 41 little bars that's going to take some time so a bar graph on the other hand if you have a bar graph external something very similar to like french fries and different heights and so forth and it's separated so that mean is in a bar graph each of these bars represents a specific category a specific item in a specific representation something that is in grass and if I were to talk about the Blues in terms of the color shirts like I'm wearing right now we have one for a baby blue royal blue indigo blue navy blue so it becomes very cumbersome so therefore if we categorize it as blue and types of blue it would go into 1 so we're consolidating and combining and that's what I hit G allow us to do okay so now using the data set we are going to review and then riq are and then using the same data points how is it going to look in a histogram that's where we're going to go to work okay I don't know why it seems like a fuzzy clear fuzzy clear I apologize for that nothing we have a date at a point to 2316 and so forth all the way up is to do what is that right on your phone is it blurry I'm just trying to get the numbers and colors sorry that isn't my car better manage his keep working on the focus of it so just really be attentive and I'll try to write a little bit larger so you can see everything make sure that we put an order is my order in order from least to greatest or us send me to climb up to make larger and put the. Next to the smallest one in Sulphur what is 11 I see another 11 I see next one is 12 Lucas the easier for me ski 16 19 do do do do do do do 22 22 again 22 again. 23 and 25 not and yet and 34 so now let's see if I have 1 2 3 4 5 6 seven eight nine 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 datapoint then we can make our IQ our box for the box-and-whisker our minimum is what minimum is 11 minimum 1111 Ann Drive the word men maximum is what a mess soda yes Max all the matches 34 Max Mr Fraser we have call Dana Point correct yes yeah so if we want to find the median exact middle where would I find the exact middle data points between what two numbers 1619 I can't hear you from 16 + 19 is that what you said yes yes mr. Brandon thank you for helping but I'm trying to ask another student so you can answer me what what is half of 12 Frasier what half of 12 is 12 / 2 mystery and how come out 6 so therefore I should go 12 3456 and then see how many I have on the far right side moving this way so I have one two three four five six so therefore the my middle is right here and if it's between 21 and 22 miss a hex what am I supposed to do I added together and then divided by 243 and then do what / / 2 so we have 21 and a half would you agree or disagree our up I haven't done the calculations I would agree you would agree who is said I would agree mr. Dionne Keller most would agree with mr. Dion tell her that it is 21 and 1/2 counting to 122 and I too would have breathed so if I divided by 2 and I get 21 and a half so now some more in here I am going put my vertical and put 21 and 1/2 and label it as my meaty and we can at least we know that is true Mr Osborne exact middle of them in this example yes but sometimes the numbers can have a a greater range between the two Center numbers when he use that is correct but in this case yes you're right and if it's back to back like this 21 and 22 when I tell the kids and for you guys is just go to the smaller one and just add a hack to it because if it is sequential in a really back-to-back all right just add a half to the smaller of the two numbers if they are both the same in the middle then use that number that is Conquering the median on the left side of the right side so if they were 22 and then another $22 back to back and that was the exact center and then your answers to be 22 text mr. Keller you have a question I'm going to say the same thing like when you said they have to be in order all right now I go to I left my median and again your Mister Parker there are these two on the left side of the median are they even number of datasets yes they are all right so where is the exact middle mister mister Frazier will you please make sure I'm going to have Mister Parker explain where is the exact middle don't give me the calculator number where is the exact middle middle of my left oh my median if I am I 21 in between 12 and 16 the middle of 12 and 16 is where I'm going to find my 21 just walking step by step there are six numbers to the left of the median 3 4 5 6 that's what he's talking about then what did you do and I know in my mind to find the middle of something it's going to have to be even on both sides of it okay Mr Fraser does that make sense what he just said yes. Can you explain what it just said in your own words if you want I tried today so whatever is said about the the middle of of the stickers on the left side he he's he's but he slipped on. check them out to find the median of the others understand everything but I heard the number six and that was your six data points in this example and tell me if I'm wrong or if I'm right in terms of what you said is that you took six data points and two fine halfway between it that means I'm going to have three on one side and 30 on the other side okay and if I had you have four on one side and four on the other side if we have 12 like we did we have six on this side and six on the right hand side now mister Parker remember I said that you noticed that it was back-to-back are these back to back no so but it is still pretty simple to find the median to it and you must have a good math teacher that's why what it's just because you're very good at War good match teacher teacher now miss Hancock are you there I don't see Miss Hancock let me see where she is Define q1 by adding 12 and 16 and I hit by 2 and you were able to add about 20 4 / 2 what you got what you got and you would get 14 am I correct or am I wrong mr. Roswell said and what you wrote don't match 24 and 12:28 and then you always say that but it's never how did you come up with that cuz it didn't work that's what my twin brother always make sure he gets a fax correct that wasn't really me being with my twin brother I was just took over for that moment 6 + 28 / 2 14 all right so that becomes your wife do you want you want so therefore I Q one is right here and I'm going to put 14 next Miss tell me how I'm going to find my Q3 upper quartile so I won't have to worry over inside an egg and you already know there is sets of data to the right and then okay so if you want to find the median of those numbers you as and the other than / 245 25 / 2 and again because they're back-to-back sequential numbers what was the hint that I told you you going to be a half that is correct Mahler other two numbers and add a half to it so it becomes 22 and 1/2 1 1/2 correct 2222 all right now let's look at the picture really carefully what lift little off in this that Kristen Ian's that's exactly what I was asking and trying to figure out if somebody cuz I said something a little off on this but Hitler picture model because we just identified knew we knew that was going to 21 and a half as our median we had to make sure just put it in there just for the purposes now we can move it around based on our q1 and Q3 so now I can use red hopefully I'm going to listen to 21 and a half is real close to 22 and a half so I'm going to move this and rewrite it as 20 don't worry guys I come prepared with another marker 21 and 1/2 and then I'm going to rewrite this and put it over here and median I'll be there all right so now we can ask we can ask ourselves what is the main what is the max what is a range what is the interquartile range the IQ are what is the mode what is the name do all of these we can answer now okay and so we practice is now my challenge to you is how do we make a histogram and I want to go there right now now to make a histogram using the data that we already put in or I am going to now create my x axis my y-axis my we are going to create intervals start with my list or my minimum which is 11 well let's make some intervals of LeSabre by fives okay 11 13/4 and 50 so 11 to 15 Matt's 16 through 20 21 M325 26 through 30 and 31 through 35 so ever can you spell consistent range of each my categories all right in the end of all be anything you wanted to be or has to be like a CERN on any type of an assessment unit assessment District assassin State exempt you from me I wanted to just get in the habit I just created making sure it's equal range representation all right yes sir but I'm doing it increments of five so you can start seeing how the data is really spread out okay so now I am because we put it in order just make a dock line out of this 11 is the first number where your Y axis that's the same number of occurrences number observed or frequency Alexis pack 1 10 3 until 44 this is so tight just that I'm going to start frequency number of frequency for there 11 BC how many to hot out of it 12 how many 12 ft with the weather 11 inches / 15 recording all about number 19 it goes in the column of 1620 how about 21 Coronavirus and you can see what I'm doing and then how many 4:20 to 3 one two free then what 1423 where is it go and then what one for the 25 and then what the 34 goes with the 31 through 35 okay Marinette am I doing this now I am just going to connect no space no space no space and because this is zero I still continue to borrow and this is how your Dot Plot is being converted to a histogram because I'm connecting just highlight the bottom and I don't mind you just High Line the bottom just on the so you can see that it's still connected so I'm using the my skills as a Dot Plot to help me with my order sequence of numbers that I've put in ascending order you can do this now there is one little question that I'm going to ask you are you ready and let's say this is the people's ages people all right and I don't care what frequency were recorded my what is the year before I car is what happens what would happen if I put 11 through 15 15 through 2020 5 until 4 why no work anniversary as well well if you have you have 11 through 15 and then 15 through 20 if you have a 3:15 in your data in your data set how would you know where to put 15 how would you not overlap our slapping the numbers that we are assigning because like I said it's very hard that if I got 15 and I had this as 15 through 20 as well where am I going to put record 15th my phone this column or this column and if you recorded them both now you have adjusted what was given to you instead of your data point and they said the same thing to if you don't if you skip a number that is correct okay so we have to be very consistent with our intervals and how we document things so that way it's a true representation of the data that is being Anri Davis set okay so now listen to let's say the frequency of let's make something up the frequency of expert video gamers wow expert video gamers or the quantity number of experts video gamers are say that the category all right and we watch please listen carefully how many people are the how many expert gamers are above the age of 20 how many people classified as an expert in Westmont Pizza near me mr. Ellis can you show over 20 if it's over 20 that mean it has to be six because and the 21 25 Rancher 6 if you're saying over everything over 20 included B6 was nobody in this age bracket was one so therefore we have to add these sick and I know I didn't continue to hear plus this one gives me all right because I'm an expert gamer I should know these things what is that mean I don't know what I'm talking about because I don't all right so it is another way of asking all right so I'm going to rewrite what I just asked you how Manny expert gamers o a r 20 are over over over 20 years of age okay are you ready for me to challenge you on another way of asking sure why how many expert gamers are at least 16 years old for how many gamers are at least 16 years old 999 Braylon Samira how many expert gamers are you at least the age of 16 all right tell me how you got that Miss Hancock he said at least six I looked at the 16 categories Screen through 20 and then so you can go above 16 because it said at least so everything F-16 adds up to nine okay so you have two year 6 years 0 and 1 so you're answering you said we're nine players and that is absolutely correct okay and the way we write it and believe it or not you recall when we did any qualities guys yes ask greater than or equal to 16 which says that the gamer the number of the gamer must be greater than 16 or equal to 6 team and I know some said 34 and a smaller number and if that was to be the man will say The Gamers age must not be greater than 16th and therefore if that's the case will be at is not going to be greater than or equal to 16 and then that refers to this grouping play if we said it this way with this question is then it goes to the right everything to the right this is like saying to you how many of you guys have ever felt a little left out when you're a little kid and you went to an amusement park and you why to ride an amazing ride and then they have a little sign that has a little measuring of a summer that's cut out of wood and they said you must be at least this height in order to go ride this ride yes honey I don't like oh my God I walk on my tiptoes because if I can't make this I can't go ride this that's the same thing what this is saying they must be greater than a certain height so if I was if it says 4 ft and you are 4 ft 5 in can you ride it yes if I was six feet tall can I ride it Coronavirus no no so this is what we call conditions we talked about this with that inequality when I assure you this concept and how to write any parties will be part of what seventh grade is going to expect you to do I guarantee it okay stop my recording for a second
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