Mr. Davison has a number of students who do really well in his English class and some who don't seem very interested at all. He is coming up with a plan for an amazing field trip to reignite his class's interest. To get a good idea of what the current level of engagement is, Mr. Davison wants to visualize the grade distribution and he thinks a bar graph is the best way to do this.

Grade |
Number of Students |

A | 15 |

B | 24 |

C | 33 |

D | 9 |

F | 6 |

How can Mr. Davison create a bar graph?

In this concept, you will learn how to create and read bar graphs.

### Creating and Reading Bar Graphs

**Data** is a set of numerical or non-numerical information. Data can be analyzed in many different ways. In this concept you will analyze numerical data using a bar graph.

One way to display data is in a **bar graph.** A bar graph shows the relationship between different values of data. Each data value is represented by a column in the graph. The categories of different kinds of data are listed along the horizontal, or \begin{align*}x,\end{align*} axis. The quantity or amount of data is listed along the vertical, or \begin{align*}y,\end{align*} axis.

Let's look at an example.

A seventh grade class recorded their favorite after school activity in a table. Create a bar graph to display the data from the table. Then, list two conclusions that can be made about the data.

Favorite Activity: |
Number of Students: |
---|---|

Watching T.V. | 9 |

Playing sports/exercising | 6 |

Reading | 7 |

Hanging out with friends | 5 |

Babysitting | 3 |

First, draw the horizontal (\begin{align*}x\end{align*}) and vertical ( ) axes.

Next, label the horizontal axis. The horizontal axis lists the different categories of data. In this case, the category will be "favorite activity."

Next, label the vertical axis. The vertical axis lists the quantity or amount of the data. In this case, the category will be "Number of Students."

Next, title the graph. The title of the graph should be short and clear. It should explain what data is presented in the graph. In this case, the title will be “Seventh Graders’ Favorite Activities.”

Then, determine the units on the vertical axis. To do this, start by reviewing the smallest and largest values in the table. The smallest value is 3 and the largest is 9. Based on these values label the vertical axis from 0-10. Further, since the values are whole numbers and between 3 and 9, a unit of 1 should be used. Therefore, the vertical axis will start at 0 and go to 10 by increments of 1.

Next, draw the vertical columns. To do this, write each activity along the horizontal axis. Be sure to leave space between each one. Then draw the column vertically until it reaches the quantity for that activity. For example, draw a vertical column to the number “9” for the activity “Watching T.V.”

Lastly, state two conclusions from the graph. To do this, analyze the data presented in the table by comparing the heights of the bars. The first conclusion is that watching T.V. is the most common favorite activity among seventh graders because the column is the highest. A second conclusion is that babysitting is the least most common favorite activity because it is the shortest column in the graph.

The first answer is the graph should look like the one below. The second answer is two conclusions that can be made from the data are: watching T.V. is the most common favorite activity among seventh graders and babysitting is the least most common favorite activity among seventh graders.

### Examples

#### Example 1

Earlier, you were given a problem about Mr. Davison, who wants to illustrate the grade distribution of all seventh grade students in English using a bar graph.

He organized the data into the following table.

Grade |
Number of Students |

A | 15 |

B | 24 |

C | 33 |

D | 9 |

F | 6 |

To make the bar graph, first Mr. Davison will draw the horizontal (\begin{align*}x\end{align*}) and vertical (\begin{align*}y\end{align*}) axes.

Next, he will label the horizontal axis. The horizontal axis lists the different categories of data. In this case, the category will be "grade."

Next, he will label the vertical axis. The vertical axis lists the quantity or amount of the data. In this case, the category will be "Number of Students."

Next, he will title the graph. The title should explain what data is presented in the graph. In this case, the title will be “Seventh Grader’s English Grade.”

Then, he will determine the units on the vertical axis. To do this, determine the smallest and largest values in the table. The smallest value is 6 and the largest is 33. Based on these values label the vertical axis from 0-35. Since the values are whole numbers and have some distance between them a unit of 5 should be used. Therefore, the vertical axis will start at 0 and go to 35 by increments of 5.

Next, draw the vertical columns. To do this, write each grade along the horizontal axis, leaving space between each one. Then draw each column vertically until it reaches the quantity for that grade. For example, draw a vertical column to the number “15” for the grade “A.”

The graph should look like the one below.

#### Example 2

The graph below shows the six countries per capita GDP for 2013. List three conclusions that can be made about the data.

The answer is three conclusions that can be made from the graph are: Australia has the highest per capita GDP of the countries listed; Greece has the lowest per capita GDP of the countries listed; and the range of the per capita GDP is approximately $44,000.

#### Example 3

The table below shows the recommended number of hours of sleep people need each day by age. Create a bar graph to display the data from the table. Then, state one conclusion that can be made about the data.

Age Group: |
Recommended Hours of Sleep: |
---|---|

Infants (0–1 years old) | 15 hours |

Children (2–5 years old) | 13 hours |

Children (6–11 years old) | 11 hours |

Teens | 9 hours |

Adults | 8 hours |

First, create the bar graph. To do this, draw the horizontal (\begin{align*}x\end{align*}) and vertical (\begin{align*}y\end{align*}) axes.

Next, label the horizontal axis. The horizontal axis lists the different categories of data. In this case, the category will be "age group."

Next, label the vertical axis. The vertical axis lists the quantity or amount of the data. In this case, the category will be "hours."

Next, title the graph. The title of the graph should be short and clear. It should explain what data is presented in the graph. In this case, the title will be “Recommended Hours of Sleep Per Day.”

Then, determine the units on the vertical axis. To do this, start by reviewing the smallest and largest values in the table. The smallest value is 8 and the largest is 15. Based on these values label the vertical axis from 0-16. Since the values are whole numbers and are less than 16, a unit of 2 can be used. Therefore, the vertical axis will start at 0 and go to 16 by increments of 2.

Next, draw the vertical columns. To do this, write each age group along the horizontal axis, leaving space between each one. Then draw the column vertically until it reaches the quantity for that age group. For example, draw a vertical column to the number “15” for the age group “Infants (0-1 years old).”

Finally, state one conclusion from the graph. To do this, analyze the data presented in the table by comparing the heights of the bars.

The first answer is the graph should look like the one below. The second answer is: one conclusion that can be made from the graph is that as people age the number of recommended hours of sleep per day decreases.

#### Example 4

The graph below shows the fifteen most populous countries in the world. List three conclusions that can be made about the data.

The answer is three conclusions that can be made from the graph are: China is the most populated country in the world, India is the second most populated country in the world, and Egypt is ranked last in the top fifteen most populous countries in the world.

#### Example 5

The graph below shows the estimated number of diabetes cases in 2000. List three conclusions that can be made from the graph.

First, analyze the graph by comparing the heights of the columns.

The answer is three conclusions that can be made from the graph are: Brunei Darussalam had the greatest number of estimated diabetes cases in 2000 at 18,000; Andora and Belize had the same number of estimated diabetes cases in 2000 at 6,000; and Antigua and Barbuda had the smallest number of estimated diabetes cases in 2000.

### Review

Use the bar graph to answer the following questions.

- How many different types of vegetables are on the graph?
- What is the range of the data?
- What vegetable was the most popular?
- Which one was the least popular?
- How many carrots were picked?
- How many potatoes?
- How many squash?
- If ten more zucchini was picked, how would this change the data?
- If each category doubled, what would the new values be?
- If each category was divided in half, what would the new values be?
- What was the total number of vegetables picked?
- What is the difference between carrots and zucchini picked?
- What scale was used for this graph?
- What interval was used in the scale?
- What is the difference between carrots and potatoes?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 11.5.