Chapter 13 · Statistics and data displays
Choose a Display for a Question
Learn to choose a bar graph, a line graph or a circle graph by naming the kind of data you have and the question you want to answer.
Data are facts that someone has collected, such as counts or measurements. A data display is a picture of the data, such as a graph.
Different displays make different things easy to see. One lets you compare amounts at a glance. Another makes a change stand out. Another shows how a total is shared out. So you have a choice to make, and it starts with two questions. What are my data? And what do I want to find out? What you want to find out is your purpose. The display must help you answer it.
No graph is drawn in this lesson. You will read a description of the data and the purpose. Then you will decide which display fits, and say why.
Here is what each of three displays shows. A category is a named group, such as a sport or a color.
- A bar graph has one bar for each category. The length of a bar shows the amount for that category.
- A line graph has one point for each time that a quantity, such as a height, was measured. The times are in order. A line segment joins each point to the next one, so a rise or a fall shows a change from one time to the next.
- A circle graph is one circle cut into slices, one for each category. The full circle stands for one total. The size of a slice shows that category's share, which is the fraction of the total that it makes up.
A circle graph needs data that are parts of one whole. This means that a single total, the whole, is split among the categories, with nothing left out and nothing counted twice.
Key concept
Fit the display to the data and the purpose
A display fits only when it matches both things: the kind of data you have and the question you want to answer. Read the description of the data and name its kind. Then name the purpose. If more than one display can hold the same data, the purpose decides which one you choose.
Before you choose a circle graph, check for parts of one whole. Read the description first. Is anything left out or counted twice? Then test with addition. If one total is split with nothing left out and nothing counted twice, the parts add up to that total. So if the amounts do not add up to the total, they are not parts of that whole, and a circle graph does not fit.
The table that follows is your guide. Each row is one display. The second column describes the data that the display fits. The third column gives the kind of question that the display answers.
| Display | Data it fits | Question it answers |
|---|---|---|
Bar graph | One amount for each separate category | Which amount is greater, and by how much? |
Line graph | One quantity measured at times in order | How does the quantity change over time? |
Circle graph | Parts of one whole: one total split among the categories | What share of the total is each part? |
Worked example
Compare amounts for categories
A school kitchen counted the lunch items it sold on Monday: tacos, salads, pasta bowls and sandwiches. The cook wants to know which item sold the most, and how many more it sold than the item that sold the least. Which display fits this purpose: a bar graph, a line graph or a circle graph?
Name the data. There is one amount, a number of items sold, for each of four lunch items. The lunch items are separate categories. They are not times, and they have no set order. You could list them any way.
Name the purpose. The cook wants to compare amounts: which one is greatest, and how far it is from the least.
Match the display. A bar graph gives each category one bar, and the length of the bar is the amount for that category. Comparing amounts becomes comparing lengths. That fits both the data and the purpose.
Rule out the other two. A line graph joins points to show change from one time to the next, but lunch items are not times. A circle graph shows shares of a total, but the cook asks about amounts, not shares.
Answer the cook from the data. The greatest amount is 52, for pasta bowls. The least is 35, for salads. Subtract the least from the greatest to find how many more. These are the two amounts whose bars you would compare.
Answer
A bar graph fits, because the data are amounts for separate categories and the purpose is to compare them. Pasta bowls sold the most, more than salads.
Worked example
See change over time
A student measured a bean plant at the end of each week. Its height was centimeters (cm) in week 1, cm in week 2, cm in week 3 and cm in week 4. She wants to see how the height changed from week to week. Which display fits this purpose: a bar graph, a line graph or a circle graph?
Name the data and the purpose. One quantity, the height in centimeters, was measured at four times in order, one week apart. The purpose is to see how that quantity changes over time.
Match the display. A line graph places the four heights in time order and joins each point to the next. Each segment stands for one week-to-week change. That fits both the data and the purpose.
Find the changes that the segments would stand for. Subtract each height from the next one. The weeks are equally spaced, so a bigger change would make a steeper segment.
Check the other two. A bar graph could hold the four heights, but separate bars show separate amounts, and the purpose is to see change. A circle graph needs parts of one whole. The heights add to 38 cm, but the plant was never 38 cm tall, so no total is being split.
Answer
A line graph fits, because one quantity is measured at times in order and the purpose is to see change. The plant grew cm, then cm, then cm, so its growth got larger each week.
Worked example
Check for parts of one whole
A class of students voted on a field trip. Each student voted for exactly one place: for the museum, for the zoo, for the science center and for the farm. The teacher wants to see what fraction of the class voted for each place. Which display fits this purpose: a bar graph, a line graph or a circle graph?
Name the data and the purpose. There is one count of votes for each of four categories. The purpose is to see each category's share of the whole class.
Check for parts of one whole. Each of the 30 students voted exactly once, so no student is left out or counted twice. Then the counts must add up to 30, and they do.
Match the display. In a circle graph the full circle stands for all 30 votes, and each place gets a slice sized by its share. That fits both the data and the purpose. A line graph does not fit, because the places are not times. Bars would show the counts, not the shares.
Find the museum's share. Write its count over the total, 30. Then divide the numerator (top) and the denominator (bottom) by 3. Dividing both by the same nonzero number is the same as dividing the fraction by 1, so its value stays the same.
Find the other three shares the same way. Every share is now in tenths, so the shares are easy to compare.
Check the shares. They have the same denominator, so add the numerators. The shares make exactly 1 whole, so the four slices would fill the circle with no gap and no overlap.
Answer
A circle graph fits, because the votes are parts of one whole and the purpose is to see shares. The museum has of the votes, the zoo , the science center and the farm .
To choose a display, name two things: your data and your purpose. Then pick the display that fits both. A bar graph fits when you compare amounts for separate categories. A line graph fits when one quantity is measured at times in order and you want to see how it changes. A circle graph fits when you want to see shares and the data are parts of one whole, with nothing left out and nothing counted twice. When the same data could go in more than one display, let your question decide.