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# Bar Graphs and Pie Charts Author: Ryan Backman
##### Description:

Calculate the percentage of categorical or qualitative data for a pie chart.

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Tutorial

## Video Transcription

Hi. This tutorial covers a specific type of graph called the bar graph. So let's take a look at some study data. So a Rasmussen Reports study from June 2012 randomly sampled 1,000 Americans and asked them if they thought that buying a home was the best investment a family could make. 540 answered yes, 245 answered no, and 215 were undecided.

OK, so this is a qualitative data set, because the answers yes, no, or undecided are all categories, so it's not quantitative data or numerical data. It is qualitative or categorical data. And a common way that qualitative data can be displayed is by using a bar graph.

So a bar graph is a chart that displays bars that are proportional in length to the frequency or relative frequency of a particular data value. So what I'm going to do now is show you how you can make a bar graph for that study data.

All right, so what we're going to do first is make a set of axes. So we need an x- and a y-axis. So we're going to do that. I'm going to use a ruler here. So we'll go down and like so. OK. And what this axis is going to be is this is going to represent our Question Responses. And the y-axis here is going to represent Frequency.

OK, so my question responses were either yes, no, or undecided. So what I'm going to do is space those evenly on my x-axis. And I'm going to put little tick marks for each of the responses. So again, this is going to represent yes. This will represent no. This will represent undecided.

Then what I need to do, to label my y-axis for frequency is I need to think about, well, what response had the highest frequency? And if you recall, that was the yes response, which had a frequency of 540. So we need to go up to at least 540.

We also need to think about what scale should we use on our axis. So I would say that we could count maybe by hundreds. So if we're going to count by 100, we would need to start at 0 and probably go up to 600, because that would be the next greatest so we could get 540 on there.

So what I'm going to do is, again, use my ruler to get equal spacing and draw in some tick marks. I'm making each of the tick marks about a half-inch apart. And if I count by-- I counted by 100, but what I'm going to do is just label every 200. So that's a pretty common way of doing that.

And now what I need to do is I need to draw bars for yes, no, and undecided. And I want my bars centered on the specific response. So my yes bar is going to go all the way up to 540. So 540 is going to be in between 500 and 600, but closer to 500 than 600.

All right, so let's go ahead and-- so again, I want the bar centered on yes. So my bar is going to go like this, and it's going to go all the way up to 540. So I'm going to draw as straight as I can down, and the other side of the bar will go like that. And I will finish off the bar like that. And then sometimes it's common to write down what the frequency is above the bar.

So now for no, no was 245. So 245 is going to be pretty close to the middle of these two marks here. So again, I'm going to-- I want it centered on no, so I'm going to mark it here and here. And then I need to go up to 240. And 240 is going to be about here and about here, and mark it like that. All right, I'm sorry, this is 245, so that's about 245 there.

And then for undecided, again, center my bar. And this is going to be centered at-- it's centered there, and it's going to go up to 215. So it's going to be a little bit shy of the last one I drew there. And again, this will be 215.

All right, so this represents a bar graph of the home as an investment data set. A couple of things about a bar graph is that I just arbitrarily assigned these values here as yes, no, or undecided. I could've easily put undecided here, yes here, and no here. These can be mixed up. So the ordering of qualitative data is generally not important. So these bars, these categories, can be labeled any way you'd like.

Again, when you're making your bar graph, make sure that you have a consistent scale on your y-axis and that your bars are centered on the category type. All right, so that is an example of how to draw a bar graph.

Another graph that is common is what's called a multiple bar graph. A multiple bar graph is a type of bar graph that can be used to compare qualitative data sets from multiple populations. And I have one that's constructed already. And this represents religious affiliation in New Zealand from 1991 to 2006.

And if you can see that, we have four religions, or four different religion responses that were possible here. So we have Christian, no religion, object to answering-- so they didn't want to answer there-- or other. And we could see that now on the year, we have '91, '96, 2001, 2006. So these represent the different populations. So we have a population from '91, from '96, '01, and '06.

Now we can see that for each of these populations, our four different categories are represented as such. This actually is going to be a relative frequency bar graph that's actually represented as a percentage. So instead of frequency here, they have percentage which they calculated using the relative frequencies. So you can see that in '91, about 70% were Christian, about 20% were none, and maybe it looks about 8% object to answering, and maybe about 2% were in the other category.

What this is nice is that you can see that from '91 to 2006, there appears to be a decline in people that expressed Christian as their religion. We can also see that no religion is consistently going up. The other thing that we can tell from this bar graph is within each year, it still does seem that the majority of people are still Christian. So what's nice about the multiple bar graph is that you can compare not only categories within each population, but you can compare one category amongst multiple populations. So this is one type of multiple bar graph that does display four different data sets within one graph.

So that's been the tutorial on bar graph. Thanks for watching.

## Video Transcription

Hi. This tutorial covers a type of graph called a piechart. So let's take a look at a study that we can get some data from. So in the 2011 study, "MetLife Survey of the American Teacher," 1,001 teachers from around the country were randomly sampled. They were asked what race slash ethnicity would they identify themselves as? The following table summarizes their responses.

OK, so if we see that-- we had the categories here. So the categories were broken down into White, Black slash African-American, Hispanic and Other. So there were 751 white teachers in this study, 123 black slash African-American teachers, 74 Hispanic teachers, and 53 teachers that classify themselves as a different race or ethnicity than the three here.

All right, so this represents a qualitative data set. So qualitative data can be nicely graphed using a piechart. So notice that a piechart is a circular graph where each data category is represented with a sector in the circle. So what is sector is-- it's kind of like a pie piece of your circle, where each pie piece will represent a different category.

So the measure of the central angle of each sector equals the category's relative frequency times 360 degrees. So remember what a relative frequency is, is what proportion of that category it is out of the total. So this gives you a percentage, or a proportion.

So if you multiply that by 360, that'll get you the correct angle to make your sector. And then put that definition into a formula. The central angle of a sector equals the relative frequency times 360. So let's use that formula to make a piechart for our race and ethnicity data.

I think it's helpful to write all of this down in a table. So we have our frequencies here. And then we're going to calculate the relative frequencies, and then the central angles. So we're going to calculate relative frequency by taking your frequencies and dividing them by n, which was 1,001.

We're then going to calculate the central angle of the sector by multiplying the relative frequency times 360. OK, so what I'm going to do-- I'm going to do those on the calculator-- and zoom in a little bit so that you can see. So what I'm going to do is take my frequency.

So the first frequency was 751. I'm going to first divide that by 1,001. That represents my relative frequency. I'm going to round that to the nearest thousandth, and then I'm going to take that times 360 to get the angle measure. So that ends up being 200 and-- about 270 degrees. I think I'm going to round all of these to the nearest degree.

Now, my next frequency is 123. So I'm going to take 123, divide it by 1,001, and then I'm going to multiply that answer by 360. So the relative frequency was 1.23 multiplied by 360. That ends up being about 44 degrees.

OK, my next frequency is 74. So I'm going to take 74 divided by 1,001. That gives me point 0.074. And then I'm going to multiply that by 360. And this is going to give me about 27 degrees. OK, and then the other category had a frequency of 53, so it's 53 divided by 1,001 times 360. And so this ends up being 0.053, and about 19 degrees.

OK, so these will represent how large I'm going to draw those central angles when I make my pie graph. So now let's use the previous table to make a pie chart. To make a piechart, a protractor should be used to accurately measure the central angles. Excel can also be used to make a piechart.

OK, so what you're always going to do is start with a circle. OK, so I drew a circle in advance here. And let's give it a label. So this is going to be Race slash Ethnicity of US Teachers. And sometimes I'll like to just put the sample size here so the reader knows how big of a sample we took. So n equals 1,001.

So now I'm going to, again, use my central angles to split these up into the different pie pieces. So notice that I have the center of my circle marked. So I'm going to center my protractor on that. And let's flip this around. And our first-- the white category has a central angle of 270 degrees.

So what I'm always going to do is just start with this reference line. So I'm just going to go straight out across, and this is really going to represent 0 degrees. And my first angle needs to be 100, and-- or, excuse me. It needs to be 270 degrees.

So what I need to do is I need to go all the way around. So that would represent 180 degrees. Now I need to go an additional 90 degrees to get to 270. Now, another way to do this is that I can just mark this at 90 here, and then I'm going to draw a line up here.

So what that means is that this is a 90-degree angle here. That central angle is 90 degrees, which means this whole angle here is 270 degrees. So I'm going to mark this as the white category. And what I like to do, then, also is to write this as a percent. So white represents 75%.

Now, this other 25% is going to be broken down into my next three categories. So the next category I'll do is the Black slash African American category, which had a central angle of 44 degrees. So what I'm going to do, again, is center my protractor on this reference. I'm going to put it on the reference line, centering it at the center of the circle. And I'm going to measure up to 44 degrees.

So this is 0 down here, so I measure up. I look on the bottom numbers here, so that's 40. 45 is this longer mark here, so 44 is about there. OK, I put a little mark there. And then I'm going to draw my line here, which is going to represent my Black slash African American category.

And I'm going to mark down what the percentage here was, which this was 12.3%. And then really I just need to draw one more line, because that's going to split this piece up into the two other categories. So I'm going to make my Hispanic category next, and that's going to represent 7.4% of the data, which is about 27 degrees.

OK, so now what I'm going to do is I'm going to center my protractor, now, on this line, and I'm going to measure 27 degrees from here. So 27-- so again, this is 0. This is 20. This is 30. So 25, 26, 27 will be about here. And then I'm going to draw a line here. And then I'm going to mark this as Hispanic, and this was 7.4%.

Now, what I can do-- if I can't quite fit the name in here, since this is a smaller sector, I can always draw an arrow, and I can put this as other. And other represented 5.3%. All right, so that represents the piechart for the ethnicity data. Sometimes what you'll see is they'll color in the sector.

So I'd need four different colors for the four different categories, and then I could make a little key off to the side, which color represents which category. So this represents the piechart for the data from the MetLife study. OK, like I said before, Excel can also do piecharts. So this is one that I did ahead of time.

The rounding might be a little bit different, but it's pretty close. So notice that they used colors here. So they used blue, red, yellow, and green. So blue represented the white population. That's also marked here as white. Black/African American, 12%. That was red. Hispanic, 7%, which was yellow. And other was 5%, which was the green category here. So again, these can also be constructed using the Excel program.

All right. So that is your tutorial on piecharts. Thanks for watching.

Terms to Know
Bar Graph

A distribution of qualitative data that displays bars that are proportional in length to the frequency or relative frequency of a particular data value

Pie Chart/Circle Graph

A distribution of qualitative data that shows the relative frequency of each category as a sector of a circle.

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