Welcome to part one of how to construct a circle graph, or pie chart.
In this video, we'll construct a circle graph or pie chart from a table of percentages and fractions.
In part two we'll take a look at creating a circle graph or pie chart from raw data.
Let's start with some background information.
A circle represents three hundred sixty degrees.  Meaning if we started with an initial ray of an angle, and we rotated it all the way around the circle,
like so, we would have a total of three hundred sixty degrees.
And then secondly, for measuring and constructing angles, we often use a protractor.
And the reason these two ideas are important.  One way to divide up a pie chart or circle graph proportionally would be to measure angles
and then construct circular sectors, or section-off pieces of the circle.
To get an idea of how this works, let's take a look at an animation.
Here we see a pie chart, or circle graph, that represents which four websites people visit the most.
If we take a look at this orange section here, notice that almost forty-six percent of the people visit this website,
therefore it must represent forty-six percent of the circle.
One way to determine this size of a circle would be to determine forty-six percent of three hundred sixty degrees, and then measure it with a protractor.
Notice as the percent increases, the percent will take up a larger section, or larger sector, of the circle.
So these pieces of the circle, called sectors, must be proportional to the percent of data that it represents.
So let's take a look at how we're going to do this.
Here are the steps to making a circle graph, or pie chart.
We're gonna first determine what percent of the data is from each category and, in this video, it will be given as a percent or a fraction.
Next, we'll determine what percent of three hundred sixty degrees represents each category.  And then, we'll divide up the circle.
So let's go ahead and give it a try.
Let's say an instructor conducts a survey of his students and he asks how many hours they studied for the last test.
And the results are given here.
If we want to construct a circle graph to represent the outcomes of this survey, we need to determine a certain percentage of the circle.
And one way to do that is to determine what percent of three hundred sixty degrees  would represent each category.
So for example, for this first category, since twenty-five percent of the people answered between zero and one,
we want to find twenty-five percent of three hundred sixty degrees.
The way we do that is we convert the percentage to a decimal, and then multiply by three hundred sixty degrees.
For the second category, we want to determine thirty percent of three hundred sixty degrees.
The third category would be twenty-five percent of three hundred sixty degrees.
And the last category would be twenty percent of three hundred sixty degrees.
Well I know twenty-five percent of three hundred sixty degrees would be one-fourth of the circle, or ninety degrees.
So this would be ninety degrees, and then so would the third category.
And so for the second category, we'll multiply point three or point three zero times three hundred sixty.
That tells us this category here would be one hundred eight degrees of the circle.
And the fourth category would be point two zero times three sixty.
Or seventy-two degrees.
So now what we'll do, is use our protractor and measure-off each angle that would represent each category of this survey.
So we'll go ahead and start by constructing the initial ray here.
The first category would be ninety degrees so that would be  from zero to ninety degrees, that would be this sector here.
We'll go ahead and label this from zero to one.
The next category would be one hundred eight degrees, so this would be ninety plus eighteen more degrees.
So maybe somewhere in here.
And this represents between one and two hours.
Now the next category is ninety degrees,
so from here to here would be seventy-two degrees plus eighteen more degrees.
So it'll be somewhere in here.
This was from two to three hours.
And then the last category here is seventy-two degrees which represents three or more hours.
Then a lot of times, they'll shade these with a nice color so they'll stand out.
So, to construct a circle graph or pie chart, it is important that we have a protractor so we can make these sectors the correct size
to represent each category correctly.   Let's go and take a look at one more.
Let's say this is the results of a survey that asks people how far they drive to work or to school.
The only difference between this one and the last one is that the results are now given as a fraction of the total instead of a percent of the total.
So the idea is going to be exactly the same.
We need to determine half of three hundred sixty degrees for this category,
one-fifth of three hundred sixty degrees for this category, and so-on.
So one way to determine half of three hundred sixty degrees is to find the product of one-half and three sixty.
Of course half of three sixty would be one hundred eighty degrees.
To find one-fifth of three sixty, we multiply one-fifth and three hundred sixty degrees.
So this is the same.
The last is one-tenth of three hundred sixty degrees.
Well I know one-tenth of three hundred sixty degrees would be the same as dividing by ten, so this is thirty-six degrees.
And then one-fifth is two-tenths, so we can just multiply thirty-six by two to find one-fifth of three hundred sixty degrees.
That would be seventy-two degrees, and this would be the same.
But let's go ahead and show how you can do this on the calculator as well.
It's the same process.  let's just check this second one.  It would be one-fifth
times three hundred sixty.
And there we go.  Okay, let's go ahead and measure these angles to divide up our circle.
Well this first category is pretty straight-forward.  One hundred eighty degrees would be half the circle.
This is the category from zero to ten.
The next category would be seventy-two degrees.
So, if we start here at one eighty, one-eighty plus seventy-two would be two hundred fifty-two.
So we'd be somewhere in here.
This is between eleven and twenty.
Now if I could, I'd probably just rotate this protractor and  measure off another seventy-two degrees.
I can't do that on this screen, so we'll go ahead and just make the best of it.
We left off at two hundred fifty-two degrees.
I'll just add another seventy-two degrees on top of that.
So I'll go over to three hundred twenty-four degrees.
Somewhere like this.
This would be from twenty-one to thirty miles.
Then the last category here would be thirty-one plus miles.
Let's go ahead and color-code each category.
Okay, that's going to do it for this video.
Next video, we'll take a look at how we do the same type of construction when we're given the raw data rather than the percentage or fraction for each category.
