Data is represented in many different forms. Using bar charts, pie charts and frequency diagrams can make information easier to digest.
There are many different ways to display data, for example:
Scatter graphs and many more...
We are looking at representing data. So we'll focus on the six main methods of representing data, and then we'll do a couple of exam style questions at the end. So I just made up some data here, right, so we can practise these methods. So let's say we've got the height of their students in a class like year seven students or something. This is the frequency.
How many students fall into each height category? There are five students between one and 1.2 metres tall, for example. And then we've also got accumulated frequency. So we just add up all of these as we go. So we've got a total of 30 students in our class.
So this is our kind of raw data that we've collected, and now we want to represent that in a nice, easy to digest form. So let's look at bar charts, first of all.
So we are interested in the frequency of students. So that's going to be on our Y axis. And we know the maximum frequency is 13. And so that's going to be my maximum. Let's call this 15.
This will be ten and this will be five to go to scale. And then to save time, I'm just going to use A-B-C and D as our categories for heights. I've just labelled these for brevity. So what we do is we look at the fact that we've got five students in the first category, category A, 15. There we go.
And we therefore just draw a bar chart like that in category B. And also, our bars should really be touching here, because this is continuous data. I should actually make sure that my bars touch each other, because we're kind of arbitrarily deciding where one category ends and the next category starts. We just made up the fact that we're going to cut it off at 1.2. Category B, we've got ten students, so I draw another bar that is ten high.
Category C is 13 students, so I draw another bar that's 13 high. And category D is just two students. So I draw a bar that's just too high. That would be my data in a bar chart. Pictograms so, again, let's say we've got category A-B-C and D.
And let's say a circle.
It might be nicer if I do a hexagon instead. Let's say a hexagon represents five students.
I may or may not regret this equals five students.
I'm going to turn it into pentagon. It's going to be nicer as a pentagon. So if we know pentagon is five students, for our first class of a one to 1.2 metres tall students, we've got five students. And so I can just draw one pentagon, simple as that. Represents five students, b is ten students.
And so I'm going to now draw two pentagons, right? And that will be five plus five gives me ten. How do we see? I've got 13 students that I need to represent, and so I know I'm going to have at least two whole pentagons, but I now need to represent three more students. And so it's going to be three five of the pentagon.
And so if I roughly do this, that's my centre, it's going to look roughly like that. There's kind of three five of the pentagon. I've kind of cut off those two fifths there. Funny D, I need two students. I know pentagon is five students, and so I need two fifths.
It's going to look roughly if that's my centre, it's going to look roughly like of that overall pentagon. First picture. Pie charts. Pie charts. We start off a big circle, like a pie, and we want to work out how we represent each of these four categories as a segment of our circle.
Well, we need to know exactly what the angle of each segment is that represents each of these four categories. And so my first category, I've got five out of a total of 30 students. So I've got five 30th of my overall classes in category A. Well, that's the same as one 6th, if I simplify that down. And I now need to work out one 6th of this total circle, where the total circle is 360 degrees.
And so I just do a 6th times 360. That gives me 60 degrees. And so if I have my protractor, I'd measure out 60 degrees, and that would be category A. We do the same thing for all the categories. We'd end up with a full circle and a pie chart, cumulative frequency.
So we're now using this third column. And so if I start off with my axes again, this time we're looking at the kind of continuous version of this data. So I start off at one metre Tool and I end up at two metres tall, which could be 1.5 in the middle. And so in this case, all we're doing is well, actually, I might just keep it in categories, keep it looking like the other chart. So we've got AB, C and D.
Let's keep it like that. And so, looking at this, I'm going to have a total of 30 and 30. So I know category A is just five, and so I can put five there. Category B is 15, and so I put 15 there. Category C is 28 and so I got 28 there and category D is 30.
We could join those up if you wanted to. That would be our cumulative frequency graph. Looking at box plots. I won't go too far in depth into box plots, but this is where we have a range, a lower quartile, upper quartile and a median. This is my minimum in my data.
This could be one student, could be 1.5 metres right there. We represent that the lower quartile is if we split our data into four chunks, this is the minimum of the middle half, the middle two chunks. And so this is my lower quartile, this is my median. So if I put all my data in a long line from smallest to largest, this would be the middle number in that long list of numbers of heights. Of course the same as the locals, but it's the maximum of that middle 50% of my data and obviously this final line is my complete maximum.
That could be a student that is maybe 1.9 metres tall. Finally, histograms histograms are slightly different, right? So in histograms the area of the rectangle represents the number. And so what we need to do is we need to first consider the width of this. So if we are looking at histograms, what we're going to have height on the x axis and this is in metres and we'll have it's called the frequency density.
Frequency density. And you'll see why in a second.
Our first histogram bar when it's going to have a width of zero two, whereas from one to 1.2. And we know that the total frequency we need to represent is five students. If I want the area of this rectangle to represent those five students, well, I know I need to be 9.2 times something times the height to get five. What's that height going to be? Well, it's going to be zero two times 25 will give me five.
And so I'm going to have a width of zero two and a height of 25. So that width there will be no .2 and the height is going to be 25. Let's say roughly that height there. I might make this smart and a thicker. Our next bar is going to have another width of zero two, whereas from 1.2 to 1.4 and we need to represent ten students in this case.
So it's a width of 0.2 times some height has to give me ten. Well I know that 0.2 times 20 times, not 20 times 50 will give me ten, right so that's 25 and this is going to be 50. And so my second bar looks like this and a width of zero point t my third bar I need to represent 13 students with the area and again it's got a width of 0.2 and so I need to work out naught .2 times. Something has to give me 13. Well, you know, on a calculator can be 13 divided by naught .2 and get 65.
So my height would be 65 for this and that's 13 students representative. Finally, if we've got 1.6 to two metres, well that's a width of 0.4 and it's got to be a height of sunburney where we do 0.4 times that height gives us two because the error has to be two for this final bar. And so I can do two divided by log .4 mega to me five. And so I know my final height is going to be five. It's going to be twice the width of the other ones but quite a bit shorter and that area represents two.
That is our histogram. Let's do a couple of example exam questions. So first of all, let's look at this pie chart. And so again we need to work out the fraction of the circle that represents ten out of half many students in total. So first of all, we need to work out the actual total number of students as fish in this case, right, say the total number of fish that we've got in our sample.
And so I can do ten plus 23 plus 39 and we see lazy on the calculator that could be 72 in total. And the first category therefore of perch fish is going to be 1072 off the total sample. So that's going to be the fraction of the circle that I need to shade in to represent this first category. So I can do 70 tooths of 360 degrees. That's my total circle.
If I didn't, sorry about saying at times 360 I end up with 50 degrees. So we're in degrees here. And so I take my projector and I'd measure out 50 degrees and I'll just do the same thing with the other two, right? So this one would be 23.72 out of a total of 360 and again I will just measure that resulting angle. My projector, let's do a question on both spots.
So we've got the minimum is eleven, that's going to be our minimum Whisker. So we'll draw that in there. Our maximum is 51. So I'll draw in that top Whisker in there. Low court order is 28.
I'll put in the start of my box there. The upcoming is 42. That's going to be the end of my box. And the median is 37. So I'll draw a line at 37 at that point there and I just put in my Whiskers and that is my box box representing data.
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