Source: Bar Graphs by Katherine Williams
This tutorial covers bar graphs. Bar graphs are a way of displaying qualitative data. As a quick review, let's look at what qualitative data is. Qualitative data is also known as categorical data. It measures qualities-- sorry, it examines qualities but it can't be measured. You can't use it to do arithmetic with it. And you're using it for descriptions.
Now with a bar graph, the count for each category, so how many things appear in each category, determines the height of the bar. And then the placement of the categories next to each other sometimes-- most of the time actually-- is arbitrary. The bars can go either horizontally or they can go vertically. And there should be some space between each of the categories. Whether you're going vertical or horizontal, there should still be some space between them. Another kind of graph, called a histogram, looks at quantitative data and then there isn't any spacing. We'll go through several examples.
This bar graph shows the relative risk of having a post-traumatic seizure after a traumatic brain injury. The bars are rising vertically. There's spacing in between each of the bars. And the categories here are mild, moderate, and severe. So the mild, moderate, and severe describe the level of the traumatic brain injury. Now it makes sense this time to order from mild, then moderate, then severe. Because here the categories have a ranking, you typically want to follow that ranking with the categories. But not all types of data are going to have that.
Then how high the bars go is telling us what that relative risk of post-traumatic seizure is. Now in this particular bar graph, they have the numbers located inside the bars as well. Sometimes you'll see it right above, sometimes it won't be there. If the number isn't there, you have to follow the height of the bar back to the axis to find out what number it corresponds to. So this here, there is no number right here. We know it's between 0 and 5. We know it's less than halfway there. So we would have to make an estimate. That's why it's nice that they've included the number because we know it's exactly 1.5.
We would do the same thing over here. If we didn't know this was 17.2, would look all the way back until we hit the axis. We would see it's between 15 and 20. It's a little bit less than halfway there so we'd make an estimate, somewhere around 17.
So another example of bar graphs on our next slide. This time the bars are going horizontally. There's little spaces in between each bar. And this time our categories are the states. Now they've chosen to organize it from the one showing the largest amount of wind generated electricity to the smallest amount of wind generated electricity. But the actual names of the states are not in any particular order. It goes from south Dakota, to Iowa, to north Dakota, to Minnesota, to Wyoming. They're not in alphabetical order. There's no real reason to put them in this order other than it shows a nice curve with our data. So that decision was pretty arbitrary. It doesn't really matter too much how we arrange it. But putting it like this can help us to see the curve and help you see the dropoff.
Another thing we can do with bar graphs is we can clump sets of bar graphs together. If we do this, we're doing a multiple bar graph. And it's really helpful for making comparisons. Here we're looking at the percent of the US households that are connected to the internet by age. So this first clump of bars shows what the world was like in 2001. And the second set of bars shows what it was like in 2009. In both bar graph sets, the colors correspond to the same thing.
On your bar graph there's usually going to be a key that tells you what the colors mean. So the blue here relates to people 16 to 44. The red relates to people 45 to 64. And the green relates to people over 65. By including both sets of data, we're able to draw a lot of conclusions. We can see that the blue is always the tallest of the three. So we can say that the age group 16 to 44 is the most connected in both 2001 and 2009.
Blue and red are usually pretty close and the green is a lot further down both times. So that tells us there's a pretty big dropoff between the 44-- sorry, 45 to 64-year-olds and the 65 plus. Now we can also see that between 2001 and 2009 all three groups showed a pretty big increase.
Here in 2001, the highest was 11.3. But in 2009, the blue, that highest group, is at 71.2. So instead of having 11.3 percent of those households connecting to the internet in 2001, 71.2 of those households are connected to the internet in 2009. So when we're adding in those extra bars and doing a multiple bar graph, there's a lot more information that's contained in our same compact space.
This example looks at flower sales in a particular store. On the vertical y-axis, we have the type of flower sold. And on the horizontal axis is the dozens of flowers sold. Now it's key here this word dozens. So when it shows the number two, that doesn't mean two flowers, it means two dozen flowers. So it's a good thing to always double check what your label is telling you. Because it could be in millions or thousands or dollars. And that's always going to give you your clue as to what it is.
So our first question says, what was the most popular kind of flower? And means what's the most popular kind of flower that this particular store sold. So looking over here, we're looking for the flower that sold the most. So the one that has the bar that's the furthest out. And that is this flower here, the carnation. So the carnation was the most popular kind of flower sold. Now be careful when you're answering questions about bar graphs to make sure you're actually answering the question.
When it says what's the most popular flower, make sure you say carnation and not 12 dozen or the bottom one, anything like that. Give the actual name, don't give any extra information. The next question says, how many more daisies then mums were sold? Now this is kind of a two part. I need to know how many daisies were sold and I need to know how many mums were sold. And then I need to do some subtraction.
So here we can see daisies. The bar goes all the way out to the 8 line. But that means eight dozen. And then on mums, it goes out to the two line, so two dozen. So then eight minus two gives me six. So six dozen more daisies than mums were sold. And again, it's important to make sure that you have that label of the dozen there, the answer six would be wrong.
The last question says, which flower about in the most money for the store? Now this question actually can't be answered by the graph that we have. It tells us nothing about money here. So even though carnation was the most popular flower and it sold 12 dozen, that doesn't necessarily mean that it earned the most money for the store. Maybe it was the cheapest flower and the roses that are really expensive brought in the most money even though they only sold two dozen.
So I had this question here kind of as a trick but to make sure that you look carefully at what information your graph has. And don't try to take out information that isn't on there. So we can't say anything about money because we don't have any information about money in our graph. So I'm going to cross it out.
This has been your tutorial on bar graphs. There are lots of different ways of using a bar graph to represent information. And it can send out kind of a lot of information from the graph itself.
Source: TABLE AND GRAPH CREATED BY KATHERINE WILLIAMS
This tutorial covers circle graphs, which are also known as pie charts. With a circle graph, that's a way of displaying qualitative data. As a quick review, let's look at qualitative data. Qualitative data is also called categorical data. It's used for qualities. You can't measure the qualities. You can't compute them with algebra. But they are giving us descriptions of the information we have.
Now with circle graphs, the count for each category, so how many things are in each category, affects the size of the sector. Now sector is just a word for that chunk of a circle, so like a pizza pie slice. So how big your count is affects how big your pizza pie slice is.
The placement of the categories is arbitrary. So when you have your circle, whether red is next to blue or blue is next to green, whatever it is you're ordering, it doesn't really matter which one goes next to each other.
And then finally, the way we're going to find out how big those pie slices, those sectors, are is we're going to multiply the relative frequency by 360. There's 360 degrees in the circle. And the relative frequency tells us what part of that total that category should contain. So by multiplying those pieces together we find out what part of those 360 degrees our categories should have. And those degrees tell us how big to make the slice. We'll work through an example together.
This example looks at the Twin Rivers Unified District student populations. In another tutorial we cover how to calculate the relative frequency. We did that based off of how many people, what the population of each of these groups was. Now in order to find the measure of the central angle, that's sector size. We're going to take the relative frequency and multiply by 360. Our total should then be 360 degrees.
So for the first one, 0.473 times 360. I get 170.28. Now when you're trying to measure these angles, you're probably only going to be able to measure to the nearest degree, if that. So I'm not going to bother reporting that 0.3, because I won't be able to measure that specifically. So I'm just going to record 170.
For the next one, 0.33, I know it's going to be smaller than 170 degrees. Because this was 0.4. I know that's taking about 47 percent of the circle. This one is 0.33, so I know it's taking about a third of the circle. So it should be about a third of 360. It should be around 120. Estimating like this ahead of doing the problem helps me to catch any mistakes I might do.
When I enter sometimes calculators you can just go .330, you don't have to put that initial 0 in. And it'll still give you the right answer. So this time I get 118.8. So that's pretty close to my estimation of 120. It's definitely less than 170. I know I've done it right. And again, I'm going around the nearest degree, so 119 degrees.
For the last one, it's 0.198, that's about 0.2. It's about 20%. So it should be about 20% of this 360 degrees. So definitely under 100, definitely under 120, probably closer to 70 or 80. 0.198 times 360 gets me 71.28. Can't really measure that specifically, I'm just going to write 71. So 71 degrees.
Now the total-- the total should be 360, because that's how many degrees are in a circle and we should be using those all up. Let's add to double check. 170 plus 119 plus 71, 360 on the nose. Sometimes, again, it'll be a little bit above or a little bit below 360 degrees. As long as we're in that area, it's OK.
Now let's see what our circle is going to look like. Our circle looks like this. Over here is the K6 group. This angle, this central angle right here in the middle, that's 170 degrees, just like we calculated on the last page. Down the bottom here is the 7-12 group. And we knew that that was going to be 119 degrees for the 7-12. And then up here is the adult group. It's the smallest one. It's the one that was 71 degrees. And this was 170 degrees.
When you're making the actual circle graph, excel, or numbers, or any kind of online spreadsheet software will calculate the degrees in the percents for you to make your graph. If you're doing it by hand, you'd need to use a protractor in order to measure out the degrees to find out how your circle graph is going to end up looking. This has been your tutorial on circle graphs.