Remember how Alex used the circle graph to make predictions? In the last Concept, Alex used the circle graph that Tania had made. Well, the entire time, he kept wishing that she had used a bar graph instead of a circle graph. Now Alex wants to take the information that Tania put in the circle graph and make a bar graph to use instead.
Here is the circle graph.
Alex looks back at the data again.
Total vegetables = 400
Carrots = 120
Tomatoes = 80
Zucchini = 60
Squash = 100
Potatoes = 40
Use this Concept to learn how to create a bar graph from a circle graph.
Circle graphs are just one of many different displays we can use to organize and present data in a form that is easy to interpret. As we have said, circle graphs are most useful when we are comparing parts of a whole or total. We can easily see which part is the biggest or smallest.
Bar graphs also allow us to make comparisons easily. Unlike most circle graphs, bar graphs let us compare exact amounts. We usually use circle graphs when dealing with percentages, and the percents of the pieces add up to 100 percent. In a bar graph, however, we use a scale to show the exact amount of each category.
Take a look at the two graphs below.
Both graphs show how Trey spends the $40 he earns each month delivering papers.
The circle graph gives this information in percents.
We can see that Trey spends 40 percent of his money on food and 10 percent on buying baseball cards. He saves the other 50% for his new bike.
The bar graph shows the same results but in a different format. The “pieces” in the circle graph are represented by bars on the bar graph. We show the categories of how Trey spends his money across the bottom. Along the side, a scale gives actual amounts of money. The height of each category bar tells exactly how much money Trey spends on that category. The food bar shows that Trey spent $16 on food and $4 on baseball cards. He saves $20 each week to put towards the new bike.
How did we get from a percentage to an actual amount of money?
When we have a circle graph, the data is presented in percentages. When we have a bar graph, the data is presented using the actual amounts that the percentages represent. To figure out a number from a percentage, we have to do a little arithmetic.
Let’s look at the first piece of data-Trey spent 40% of $40.00 on food.
We need to figure out how much that 40% of 40.00 is. To do that, we can write a proportion. A proportion compares two fractions, so first we convert our percentage to a fraction:
Notice that the fraction shows the partial value on top, and the total on the bottom. Next, we want to know how much of the $40.00 is 40%. We write a second fraction with the total number of dollars Trey has to spend on the bottom, and a variable on top to represent the part of his total money we want to know:
Here is our proportion.
You can see that we cross multiplied and divided to get our answer. Trey spent $16 of his $40.00 on food.
If you look back at the bar graph, you can see that this is the actual amount from the bar graph.
Once you have converted all of the percentages to actual numbers, you can build a bar graph just as you did in an earlier Concept.
Now let's practice.
John spent 15% of $20.00 on candy. How much did he spend?
Susan ate 45% of 20 carrots. How many did she eat?
Solution: 9 carrots
Kelly sold 55% of 60 zucchini. How many did she sell?
Solution: 33 zucchini
Now back to the original problem.
We can draw some conclusions about the data to help Alex make sense of the graph. Let’s look at a few questions to help us make sense of the vegetable growth.
What is the largest group of vegetables grown?
- According to the graph, the carrots were the largest group grown.
If they were to double production next year, how many of each type of vegetable would be grown?
- Carrots = 120 to 240, tomatoes = 80 to 160, zucchini = 60 to 120, squash = 100 to 200, potatoes = 40 to 80.
Which vegetable was the smallest group?
- The smallest group is potatoes.
Alex and Tania can look at two things as they work to increase vegetable growth. Our graph doesn’t tell us why they only grew 40 potatoes. They can analyze whether insects hurt their crop or whether or not they planted enough. The circle graph gives them a great starting point for future planning.
Alex prefers bar graphs to circle graphs. Let’s use the data from the circle graph to build a bar graph.
- The first thing to see is that the range of growth is from 40 to 120. We can make our axis on the left hand side have a range from 0 to 120 in intervals of 20. This will include each category of vegetable.
- Here is our bar graph.
Alex and Tania now have two different ways to examine the same data. Planning for next year’s garden is a lot simpler now.
Here are the vocabulary words in this Concept.
a visual display of data that uses percentages and circles.
a part of a whole represented by a decimal point.
a part of a whole written out of 100 using a % sign
to examine data and decide future events based on trends.
If you think back through the last several concepts, you have learned many different ways to display data. Let's put that altogether.
Frequency Table-shows how often an event occurs.
Line plot-shows how often an event occurs-useful when there are a lot of numbers over a moderate range.
Bar graphs-useful when comparing one or more pieces of data
Line graph-shows how information changes over time
Circle graph-a visual way to show percentages of something out of a whole.
Take a minute to write these notes down in your notebooks.
Choose the best data display given each description below.
A tally of how many people ate ice cream cones in one week.
The number of people who attended Red Sox games for 2002, 2003 and 2004.
Percentages showing where people choose to go on vacation.
Here are videos for review.
Khan Academy: Reading Bar Graphs
Khan Academy: Reading Pie Graphs (Circle Graphs)
Directions: Use the following circle graph and proportions to answer each question.
Three hundred students were surveyed to find out their favorite school lunch.
1. How many students chose hamburgers as their favorite lunch?
2. How many students chose chicken fingers as their favorite lunch?
3. How many students did not choose hamburgers?
4. How many students chose pizza as their favorite lunch?
5. How many students chose grilled cheese as their favorite lunch?
6. How many students did not choose grilled cheese or pizza?
7. How many students did not choose chicken fingers as their favorite lunch?
8. How many students were undecided?
9. Given your answers to numbers 1 - 8, what interval would make sense to use as the vertical axis of the bar graph?
10. What is the range of the data?
11. What would you use to label the horizontal axis of the bar graph?
12. Would the bar graph use numbers of students or percents?
13. What proportion did you use to figure out each value in numbers 1 - 8?
14. True or false. Any circle graph can be drawn as a bar graph.
15. True or false. Bar graphs use actual numbers and circle graphs use percents.