now we're going to see how to create a circle graph from some given data and like so many things in mathematics this is going to be best demonstrated with an example so here's the example problem after being hired by the CIA Jake spent money for his mission as follows uh on travel for for plane tickets he spent $1,520 on spy cameras he spent $1,260 he spent $975 on Kung Fu lessons $700 on a bulletproof vest and $145 on pizza so this is all of his expenditures and we want to make a circle graph or a pie chart of this data and here's how we do it before we arrange the data on the pie chart we need to figure out how big to make each sector of the of the circle so we set up a table something like this now I'm going to list all the amounts the different things the the different amounts of money that he spent on those different items or those different categories in this column right here so I'm just going to put the numbers in from the problem on travel he spent $1,520 on cameras he spent $1,260 on Kung Fu lessons he spent $975 and on the bulletproof vest just abbreviated that there bullet proof vest is $700 and pizza he spent $145 and then I add those up to get a total so the total expenses if you add those numbers up the total comes out to $4,600 now we need to figure out what percentage of the total each of these is so the the travel was $1,520 that's $1,520 out of the total of4 600 so we'll pull up the calculator here and we'll just put in those numbers 1,520 divided by 4600 and that gives me 330 so that that's 33% or 33043 and so on but we'll call it 33% so 33% of the total was spent on on travel and then we'll do the same thing with the other categories 1260 divided by 4600 comes out to. 27 or 27% of the total and on the Kung Fu we do 975 okay that much divided by the total of 4600 and that comes out to. 21 so that's 21% and and then the bulletproof vest cost $700 out of a 4600 total so that's 700 divided by 4600 and that comes out to 15% and pizza he spent 145 out of the total $ 4600 on pizza and that comes out to 3% and those should add up to 100% And if you add them up they actually add up to 99% and that's because these values were rounded some they don't quite add up to 100% And that's okay that number should be close to 100 though every single time all right now those are percentages now we need to figure out how many degrees how big the angle should be for each of the sectors so let's look at this first one up here on the on the top row the travel he spent 33% of the money on travel so the section or the sector of a circle representing travel should be 33% of the circle well a circle has 360° so we need 33% of that so I need to calculate 33% of 360 and that will be the number of degrees for the travel so I'll type in 33 * 360 and that comes out to 11 18.8 we'll round that to 119 so on this on the sector on the on the pie chart or the circle graph when I actually draw the sector representing the travel it will have to be an angle of 119° and then we'll do the same thing with the other categories uh 27% of the money was spent on spy cameras so we need 27% of the circle or 27% of the total 360° so I calculate 27 time 360 remember time T times typically means of when I say 27% of 360 that means 27% times 360 and that's 97.2 we'll round that to 97 and then the other ones I'll give you the the answers here 21% of a full circle 21% of 360° is 7 76° and 15% of a full circle comes out to 54° and 3% of a full circle comes out to 11° 11° is the the angle for the for this last category here the pizza and if we add those up those should add up to 360 and they come pretty close they add up to 357 if you add all of these numbers up they don't total up to 360 any and again that's because of rounding error and that's okay they come pretty close now we just need to draw our circle with uh sectors marked off with those measurements so here's our Circle and we'll start off we'll draw a line across here and it's usually easy to start with a horizontal line there and then I'll measure around here and really um you would want to take your protractor and line it up with the bottom Edge there and get this angle accurately and it needs to be 119° and that puts us to about there and I'm going to write in here I'm going to write travel 33% because that's that's 33% of the total right there for the travel and then and and this angle right here is 119° or 33% of the entire circle now the cameras this my cameras were 27% so I'm going to and that came out to be uh 97° so you need to make another angle here and again you want to measure this with a protractor so that this angle right here comes out to be 97 deges and then we write here we'll write cameras and you don't write the angle here let's write 27% you can write the percentages or you might write the actual number $1,260 there um but it's also very common to write the percentages and then the Kung Fu lessons were 76° so we need an angle down here about right there um and again measure this with the protractor that should be 76° and the Kung Fu lessons were 21% and then the bulletproof vest was 15% and that angle was uh 54° and um I need to label this one Kung Fu and then there's not enough room to write in this sector so we just put a little line here and we can write outside Pizza is 3% and this angle right there should be 3% of the total or 11 degrees and it's pretty common when the sector is really small like that to have the data written there outside the circle like that but that's a circle graph that's how you create one and um and keep in mind that those angles should all be drawn accurately using a protractor or you could put the data into a spreadsheet and most spreadsheet programs will create a nice picture like this with different colors in the different sectors um colorcoded with a little key and accurately drawn angles