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Bar Graphs, Frequency Tables, and Histograms

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Represent Real-World Data Using Bar Graphs, Frequency Tables and Histograms
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The students at Smith Middle School returned to classes and found out that there was a big surprise. Wood shop had been cancelled from the curriculum.

“How could they have cancelled wood shop?” Kyle asked when looking at his schedule. “I have been waiting all year for this.”

In the past, only the students in the seventh and eighth grades were allowed to take wood shop. Many students spent all of sixth grade waiting for wood shop.

“I know, I was waiting for it too,” Sarah said.

“There must be a mistake,” Tanisha commented.

However, there wasn’t a mistake. The administration was sure that there wasn’t enough student interest to continue having wood shop.

This set the students in the seventh and eighth grade on a mission. That very first day after school, the students held their own meeting on the football field. They decided to gather data and prove to the administration that wood shop was a necessary part of the curriculum.

Over the next few weeks, the students worked hard to gather data about wood shop. They learned that in 2008, there were 30 out of 100 seventh graders and 40 out of 100 eighth graders who had participated in wood shop. Then in 2009, the numbers had increased. There were 40 seventh graders and 58 eighth graders who had participated.

“This is great!” Kyle said. “Now we can prove that wood shop is wanted!”

“Yes, but I think we should draw a chart to show our results,” Tanisha said.

This is where you come in. In this Concept, you will learn how to draw different types of graphs to display data. Pay close attention because at the end of the Concept you will need to draw a bar graph to show the data that was collected.

Guidance

Real-world data can be easily and accurately represented by using bar graphs, frequency tables and histograms. Let’s look at how to work with these data displays.

The data table below depicts the ages of twenty of our nation’s presidents at the time of Inauguration. Create a bar graph, frequency table, and histogram to display the data.

To create a bar graph, first draw a horizontal (x) and vertical (y) axis.

Label the horizontal axis with each president’s last name.

Label the vertical axis with intervals of two, beginning with the number thirty.

Next, draw a vertical column to the appropriate value for each president.

Now, create a frequency table by drawing three columns. Designate the first column for intervals of four. The middle column is to tally the ages. The final column depicts the total frequency for each interval.

Finally, create the histogram. To create a histogram, first draw a horizontal (x) and vertical (y) axis. Label the horizontal axis with the intervals depicted on the frequency table. Label the vertical axis by ones. Draw a vertical column to the appropriate value for each interval on the horizontal axis. Recall that there is no space between the vertical columns on a bar graph.

Examining data using bar graphs, histograms and frequency tables can help us to understand information in a visual way. For people who learn in a visual way, using data displays is a great way to tackle such a task!

Now use this bar graph to answer the following questions about our presidents.

Example A

How many of our presidents were sixty-one years of age or older at the time of the Inauguration?

Solution: Seven presidents

Example B

What was the most popular age for a president at the time of the Inauguration?

Solution: Fifty-seven years old

Example C

What was the age of the youngest president? Who was it?

Solution: Forty-three years old, Kennedy

Now let's go back to the dilemma at the beginning of the Concept.

It is time to draw a bar graph to represent the data. Remember that the bar graph that you draw needs to show the data for 2008 and 2009.

To create a bar graph, remember you will need a vertical axis and a horizontal axis.

Because there are 100 students in both the seventh and the eighth grade, you will be able to figure out the intervals for the vertical axis. The horizontal axis should show the numbers of seventh and eighth graders for both 2008 and 2009.

Here is a bar graph to show the data.

This bar graph will help the students to show the administration how popular wood shop has become!

Vocabulary

Data
information that has been collected regarding an occurrence or an event.
Bar Graph
is a graph that uses columns to compare quantities or amounts.
Frequency Table
is a display that summarizes data by depicting the number of times that a data value occurs.
Histogram
is a display that shows the frequency of data values on a graph.

Guided Practice

Here is one for you to try on your own.

Use this histogram and figure out how many students spend between 1 hour and 1 1/2 hours studying.

Solution

If you look at the histogram, you can see that the horizontal axis represents the hours that students spend studying. The vertical axis represents the number of students who study for each period of time.

Given this histogram, there are 35 students who spend between 1 hour and 1 1/2 hours studying.

Video Review

Khan Academy Histograms

Practice

Directions: Use the histogram from the Guided Practice to answer the following questions.

1. How many students spend less than 30 minutes studying?

2. How many students spend greater than 60 minutes studying?

3. How many students spend greater than 90 minutes studying?

4. How many students spend between 2 and 2 1/2 hours studying?

5. If this histogram is the result of a survey, was the number of students surveyed greater than 100?

Directions: Use this bar graph to answer the following questions.

6. If each girl could only vote once, what was the total number of girls surveyed?

7. If each boy could only vote once, how many boys were surveyed?

8. What fraction of the girls surveyed chose track as their favorite sport?

9. What fraction of the girls surveyed chose soccer as their favorite sport?

10. What percentage of the girls surveyed chose track and soccer as their favorite sport? You may round to the nearest whole percent.

11. What fraction of the boys chose football as their favorite sport?

12. How many boys and girls were surveyed in all?

13. True or false. Basketball is the least popular sport among girls.

14. True or false. It is also the least popular among boys.

15. What is the most popular sport among girls?

16. What is the least popular sport among boys?

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