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Introduction

The Harvest

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.

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.

Alex is going to make a bar graph to show the vegetable counts from August.

Then they want to make one double bar graph to show both months on one graph.

Do you know how to design one of these bar graphs?

Tania and Alex can’t remember what to do to draw them.

In this lesson you will learn all you need to know to help Tania and Alex solve their graphing dilemma.

What You Will Learn

In this lesson you will learn how to do the following things.

  • Make a bar graph to display given data.
  • Make a double bar graph to display and compare given data.
  • Make multiple bar graphs to display and compare given data.
  • Collect, organize, display and analyze real-world data using frequency tables and bar graphs.

Teaching Time

I. Make a Bar Graph to Display Given Data

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
5^{th} 51
6^{th} 88
7^{th} 75
8^{th} 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 it’s time for you to draw your own bar graph given a set of data.

1. Below is data regarding the number of visitors that went to the botanical garden in four days. Draw a bar graph to display the data, don't forget to label.

Day 1 = 310

Day 2 = 600

Day 3 = 550

Day 4 = 425

2. Which scale did you use tens, hundreds or thousands?

3. Which day has the longest bar?

4. Why is that?

Take a minute and check your work with a peer. Do the bar graphs match? Which scale did you use? Compare the graphs; are they both accurate? Why or why not?

II. Make a Double Bar Graph to Display and Compare Given Data

We just learned how to make a single bar graph, but what about a double bar graph?

What is a double bar graph?

A double bar graph is used to display two sets of data on the same graph. For example, if we wanted to show the number of hours that students worked in one month compared to another month, we would use a double bar graph.

The information in a double bar graph is related and compares one set of data to another.

How can we make a double bar graph?

We are going to make a double bar graph in the same way that we made a single bar graph except that instead of one bar of data there will be two bars of data. Here are the steps involved:

  1. Draw in the two axes. One with items we are counting and one with the scale that we are using to count.
  2. Decide on the best scale to use given the data.
  3. Draw in the bars to show the data.
  4. Draw one category in one color and the other category in another color.

Take a minute and copy these steps down in your notebook.

Now, let’s continue by looking at an example.

Example

Here is the data for the number of ice cream cones sold each week at an ice cream stand during the months of July and August.

July August
Week 1 500 800
Week 2 800 900
Week 3 700 600
Week 4 900 800

We want to create a bar graph that compares the data for July and August.

First, we will have two axes.

Next, we can write in the week numbers at the bottom and use a scale for the side.

Since we have ice cream cone sales in the hundreds, it makes sense to use a scale of hundreds from 0 to 1000 counting by hundreds.

Now we can draw in the bars. Let’s use blue for July and red for August.

Now that you have learned how to draw a double bar graph, here is one for you to do on your own.

1. Draw a double bar graph given the number of books sold during weeks 1, 2 and 3 in September and October.

September October
Week 1 1000 1500
Week 2 2000 1500
Week 3 500 1000

2. What can you conclude about book sales during weeks 1 and 2 in the month of October?

3. What can you conclude about book sales during the second week of September?

Take a minute to check your work with a peer.

III. Make Multiple Bar Graphs to Display and Compare Given Data

We just finished making a double bar graph. Think back to the problem about the ice cream sales at the ice cream store.

Let’s look at that double bar graph once again.

We can look at this bar graph and compare the ice cream sales during the months of July and August.

What if we wanted to compare ice cream sales during September and October with the sales from July and August?

This is an example where we would need to make a second double bar graph. We need to use the same scale so that we can visually examine both sets of data.

We can use the same steps as before.

Here is the data on ice cream sales during September and October for weeks 1 – 4.

September October
Week 1 600 400
Week 2 500 200
Week 3 400 100
Week 4 300 100

Now we can take this data and design a double bar graph.

Now we can work on drawing conclusions by comparing the two double bar graphs.

Look at each double bar graph and answer the following questions about the ice cream sales.

  1. Which week in the month of July had the best sales?
  2. What conclusion can you draw about ice cream sales during the month of October?
  3. Did week 2 in September or week 2 in July have better sales?

Take a minute to check your work with a peer.

Real Life Example Completed

The Harvest

Now that we have learned all about bar graphs and double bar graphs it is time to help Tania and Alex.

Let’s review our original dilemma.

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.

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.

Alex is going to make a bar graph to show the vegetable counts from August.

Then they want to make one double bar graph to show both months on one graph.

As usual, the first step is to go through and underline all of the important information. This has been done for you.

To complete this problem, we need to make 3 different bar graphs, one to show July’s counts, one to show August’s counts and one to show the two counts compared on one double bar graph.

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, we can help Alex make a bar graph to represent the August harvest. 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.

To compare both months together, we organize the data in a double bar graph. The key is to use the same scale so that it is easy to compare each quantity. You can also see how the harvest amounts changed during each month.

Here is the double bar graph.

Vocabulary

Here are the vocabulary words that were used in this lesson.

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.
Double Bar Graph
A graph that has two bars for each item counted. It still uses a scale, but is designed to compare the data collected during two different times or events. A double bar graph is a tool for comparisons.

Technology Integration

Khan Academy Reading Bar Graphs

Other Videos:

  1. http://www.teachersdomain.org/resource/vtl07.math.data.rep.attentscal/ – This is a PBS video clip from the show Cyberchase that shows how to build and create a bar graph.

Time to 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?

Class Activity Project

Take a survey in your class. Ask students about their summer activities. The categories are beach, camping, pool, summer camp, or other (for anything else).

Once you have completed the survey, create a table to show your results. Then design a bar graph to show your results. Also design a double bar graph to compare girls and boys.

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