2.11: Bar Graphs
Have you ever looked at a bar graph? Bar graphs are used all the time.
It is the first week of September and while there are still vegetables growing in Alex and Tania’s garden, there has been a lot of harvesting during the months of July and August. Tania and Alex have kept track of how many vegetables were harvested each month. Here is their data:
July | August |
---|---|
30 carrots | 60 carrots |
10 tomatoes | 20 tomatoes |
25 zucchini | 30 zucchini |
15 squash | 25 squash |
10 potatoes | 20 potatoes |
Tania and Alex want to display their data. Tania wants to make a bar graph that shows the data for July. Alex is going to create a display for August.
Guidance
We make bar graphs from a set of data. It is called a bar graph because it is a visual display of data using bars. The number of items tells us how many bars the graph will have. The amount of each item tells us how tall each bar will be. Let’s make a graph of the following data. It tells how many hours students in the fifth, sixth, seventh, and eighth grade classes volunteered in a month.
Class | Number of Hours |
---|---|
\begin{align*}5^{th}\end{align*} |
51 |
\begin{align*}6^{th}\end{align*} |
88 |
\begin{align*}7^{th}\end{align*} |
75 |
\begin{align*}8^{th}\end{align*} |
39 |
You can see that this information has been written in the form of a frequency table. It shows us how many hours each class has worked.
Now we can take this and draw a bar graph to show us the information.
To make a bar graph, we draw two axes. One axis represents the items, and the other represents the amounts. The “items” in this case are each class. The amounts are the number of hours the classes worked. For this example, our axes might look like the graph below. Remember to label each axis!
Next, we need to choose scale for the amounts on the left side of the bar graph. We can use scales of 1, 2, 5, 10, 20, 50, 100, 1,000, or more. To choose the scale, look at the amounts you’ll be graphing, especially the largest amount. In our example, the greatest value is 88. If we used a scale of 100, the scale marks on the left side of the graph would be 0, 100, 200, and so on. It would be very difficult to read most of our amounts on this scale because it is too big. Every amount would fall between 0 and 100, and we would have to guess to be more specific! On the other hand, if we used a small scale, such as 5, the graph would have to be very large to get all the way up to 90 (since our greatest value is 88).
It makes the most sense to use a scale that goes from 0 to 90 counting by 10’s. That way each value can easily represent the hours that each class worked.
Here is what the graph looks like with the scale filled in.
Now we can draw in the bars to represent each number of hours that the students worked.
Look at how easy it is to get a visual idea of which class worked the most hours and which class worked the least number of hours. We can use bar graphs to give us a visual sense of the data.
Now let's practice by using a bar graph to analyzing data.
Example A
Which state has the highest average price for gasoline?
Solution: Hawaii
Example B
Which state has the lowest average price?
Solution: Missouri
Example C
Which state has the second highest average price?
Solution: California
Tania and Alex want to display their data. They have decided that bar graphs are the best way to do that. Tania is going to make a bar graph that shows the vegetable counts for July.
Let’s start by helping Tania to make a bar graph to represent July’s harvest. Here are her counts.
July
30 carrots
10 tomatoes
25 zucchini
15 squash
10 potatoes
Now we can make the bar graph. We know that the amounts range from 10 to 30, so we can start our graph at 0 and use a scale that has increments of five. Here is the bar graph.
Next, Alex can create his bar graph for August. Here is his data.
August
60 carrots
20 tomatoes
30 zucchini
25 squash
20 potatoes
Notice that these numbers are different than the ones Tania had. Here our range is from 20 to 60. Because of this, we can use a scale of 0 to 60 in increments of five. Here is Alex’s bar graph.
Vocabulary
Here are the vocabulary words in this Concept.
- Bar graph
- A way to organize data using bars and two axes. One axis represents the number of each item and the other axis represents the item that was counted.
Guided Practice
Here is one for you to try on your own.
Based on this graph, how many seventh graders have a favorite activity of watching tv?
Answer
First, you can look at the column that refers to television. Then look at the vertical axis.
9 seventh graders have "watching tv" as their favorite activity.
Video Review
Here is a video for review.
Khan Academy Reading Bar Graphs
Practice
Directions: Use the bar graph to answer the following questions.
1. How many students were asked if they have summer jobs?
2. What is the range of the data?
3. What are the three jobs that students have?
4. How many students do not have a summer job?
5. How many students babysit?
6. How many students do yard work in the summer?
7. How many students work at an ice cream stand in the summer?
8. If ten more students got a job this summer, how many students would have summer jobs?
9. If each category had double the number of students in it, how many students would have summer jobs?
10. How many students would babysit?
11. How many students would work at an ice cream stand?
12. How many students wouldn’t have a summer job?
13. What scale was used for this graph?
14. What interval was used in the scale?
15. What is the difference between working at an ice cream stand and doing yard work?
Analyze
To analyze is to look at data and draw conclusions based on patterns or numbers.bar graph
A bar graph is a plot made of bars whose heights (vertical bars) or lengths (horizontal bars) represent the frequencies of each category, with space between each bar.Image Attributions
Here you'll learn how to make a bar graph to display given data.
Concept Nodes:
Analyze
To analyze is to look at data and draw conclusions based on patterns or numbers.bar graph
A bar graph is a plot made of bars whose heights (vertical bars) or lengths (horizontal bars) represent the frequencies of each category, with space between each bar.