NOTE: These videos were prepared when the Census at School Project was managed by Statistics Canada. Most of the information is still relevant.
Duration: 10:57 min.
In this episode, we'll look at how to use TinkerPlots to create various sorts of graphs and find the mean, median and mode.
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Hi, I’m Angela McCanny. In this episode, we’ll look at how use TinkerPlots to create graphs and find the mean, median and mode, using your class dataset.
TinkerPlots is distributed by Key Curriculum Press and is used in many school boards across Canada. I am assuming that you have already imported your class dataset into TinkerPlots. So, let’s go open that file.
First, open the TinkerPlots program. Then, from the File menu, go to Open, and in the Look in box, find the location where you saved your class dataset file in TinkerPlots.
On the screen, we are looking at the data cards for a group of grade 6 students. These cards hold the answers from the Census at School survey for this class.
Click on the arrows to see more student answers. The data cards allow us to look at the answers one student at a time. If we want to see all the students results together, we can make a table.
To make a table, click on the Table icon in the top grey menu bar and drag it into your workspace. The table lets you see all the answers for your class at one time. We can make the table bigger by dragging on the bottom right corner. To see all of the columns in the table, move the bottom slider to the right. To see all the students, move the slider up and down.
Now that we have the data, we are ready to make a graph. Let’s get the table out of the way by making it a little smaller, and moving it beneath the data cards.
TinkerPlots calls graphs “plots”, so to create a graph, click on the Plot icon in the top grey menu bar and drag it into your workspace.
Now, we see a bunch of circles in the plot window. If I click on these circles, we can see the case cards changing and different rows being highlighted in the table. So what do these circles represent? Each one is a student with all of his or her data attached. Right now they aren’t organized any particular way; it’s like they’re all standing in a bunch in the playground.
So to create a graph, we need to drag an attribute onto the horizontal axis. Let’s make a graph to show the gender breakdown of this class. From the data cards or the table, click and drag the “gender” attribute onto the horizontal axis. Click on gender and keep the mouse pressed down as you drag. You will see a target zone box appear along the vertical axis. Ignore this and keep dragging until you get to the target zone box for the horizontal axis. Release the mouse button. And voila, the class is divided by gender.
It’s hard to see which group has more, though, so we can organize the points better by clicking the vertical Stack button in the top menu bar. A number line appears along the vertical axis to give us the count and we can easily see that there are more female students than male students in this group.
You can also find the number of each gender by clicking on the N icon to see the number: 17 girls and 15 boys. Click on % sign to see the percent for each gender.
If we want to make a new graph we can mix up the data by clicking the arrows at the bottom left of the plot.
So, let’s make a new graph. We’ll graph the eye colour this time.
So click on eye colour and drag it onto the horizontal () axis and click Stack. It’s easy to see that the most common eye colour is brown. This most common response is called the mode.
Notice the order that the answers are displayed in: blue, brown, green, other. They’re in alphabetical order. What might be a better order to display the data? How about greatest to least? We can drag each label to its correct position by clicking on the word (not the circles) and dragging it to where it makes most sense.
What type of graph does this graph most resemble? Some might say a pictograph, with each individual circle representing one student. Suppose we wanted to make it into a bar graph.
To change the graph type, click on the arrow beside the Circle Icon and select Fuse Rectangular. Now it’s a pretty good bar graph. It could use a title, so we can insert a text box and type in our title. Let’s say “Eye Colour in Grade 6B”. Much better.
So far, we have been graphing categorical data, that is, data whose responses come in categories. For example, the responses for gender comes in two responses—male or female—, and eye colour has four colour categories — blue, brown, green and other. Categorical data is well suited to being displayed in bar graphs and in circle graphs, so let’s see how we can transform this graph into a circle graph.
To make a circle graph, click on the arrow beside Fuse Rectangular and select Fuse Circular. We see four separate circles. To form these into a single circle, select one circle and drag all the others into it. That’s better, but not great. Notice that all the responses are placed randomly around the circle. In a circle graph, we want the like responses to be grouped together so we can compare the total amounts for each category. To group them, click on the Order icon in the top grey menu bar and all the like coloured segments are grouped together. Now we can easily see the most common and least common colour and compare the frequency of each colour with the others.
Let’s mix up the graph again and take a look at one more graph of categorical data. This time we’ll look at the students’ favourite subjects and then see whether there is any difference between the favourite subjects of the girls compared to the boys.
Use the slider to move down the table until you see the column for favourite subject. You might have to make the column wider to see the whole column label. Drag the favourite subject attribute onto the horizontal axis and click Stack. It looks like math is the favourite for this group with physical education as a close second. If we click the number button (n), we can see the numbers and yes, we were right about the favourites.
I wonder if this is still true if we check the responses for boys and girls separately. So, this time, we leave favourite subject on the horizontal axis, and drag gender onto the vertical. What do we see? Math and physical education stayed the favourites for the boys (click on % and see 33% and 27%). However, the girls have distinctly different favourites in this class: Art and then English in first and second places. Interesting.
So far, we have only graphed categorical data, but we can also graph numeric data in TinkerPlots. Let’s see what we can find out about the heights of these students. Go to the table and drag the height information onto the horizontal axis. TinkerPlots will always divide numeric data into two intervals. Usually, it will be more helpful for us to see the data divided up into smaller intervals. To separate the data, click on a circle and drag it to the right. Keep doing this until a continuous number line of heights is created, and click Stack.
It looks like we have a cluster of students around 146 cm. tall, and another group around 152 cm tall. When there are two equally common responses, we call the data “bi-modal”. Notice that we’ve been able to find the mode for both categorical and numeric data. However, the other two measures of central tendency, median and mean can be found for numeric data only. And once we have graphed it, TinkerPlots can find these calculations quite easily.
To find the median— that is, the middle value—, go to the Averages icons in the top grey menu bar. If you hold the cursor near the upside down red T, the word median will appear. Click on the median symbol and it appears on the graph to show the median. It looks like about: 150 cm. To read that number exactly, we can insert a movable reference line, from up here in the menu bar and line it up with the median symbol to get an exact value. The median is: 150.2 cm.
Similarly, for the mean—which most people call the “average”. To find the average height, click on the blue triangle in the grey menu bar and the triangle appears on the graph; it is slightly lower than the median in this case. If we drag the reference line over, we can see that the average height for these students is 149.5 cm.
If we want to compare the average heights for the boys and the girls in this class, drag gender from the table to the vertical axis. And we can see that for this group, the girls are taller on average than the boys. For grade 6 students, this might be pretty typical.
The last graph I would like to show you is a graph that compares numeric data on both axes. We call this a scatter plot.
Let’s graph the students’ height and foot length data, and try to answer the question: “I wonder if tall students also have big feet? Another way to ask this is “I wonder if there is a connection between height (being tall) and foot size (having big feet)?”
Mix up the plot. Drag height to the horizontal axis, and drag it out to a complete number line. Now drag foot size to the vertical axis, along the left side of your plot. Again, separate the foot sizes into smaller groupings by dragging a circle to the top of the screen.
What do we see on the graph? The data points are arranged in a line going upwards to the right. In general, the shorter heights have smaller foot sizes and the taller heights have longer foot sizes. Since the data looks like it is forming a slanted line on the screen, it means there is a connection or relationship between the attributes. This is also called a trend or a correlation.
So, what do you think? Is it true? Do tall students have big feet in this class?
This is just a sample of the types of data exploration you can do using your class dataset and TinkerPlots.
Students generally figure out how to use TinkerPlots with no more than the instruction I have just given you. But if you would like further ideas and instruction, you can find them on Key Curriculum Press’ TinkerPlots website.
Very soon you will be able to come up with your own ideas for data discovery using TinkerPlots. Enjoy!