An innovative chef decides to test five different recipes to see if they receive a favorable response on his menu. He selects one for fish, one for chicken, one for beef, a pasta dish, and a vegetarian dish. After the recipes are served to a dining room of 35 people he gathers their responses about whether they would order that entree again. He then tallies the results. How can he compare the yes/no results for each recipe? How can he compare the results of the recipes against each other?

### Watch This

First watch this video to learn about double bar graphs.

CK-12 Foundation: Chapter8DoubleBarGraphsA

Then watch this video to see some examples.

CK-12 Foundation: Chapter8DoubleBarGraphsB

### Guidance

In previous Concepts, you studied both histograms and bar graphs. Remember that histograms have measurements on the horizontal axis \begin{align*}(x)\end{align*} and frequencies on the vertical axis \begin{align*}(y)\end{align*}. A bar graph, on the other hand, displays categories on the horizontal \begin{align*}(x)\end{align*} axis and frequencies on the vertical \begin{align*}(y)\end{align*} axis. This means that bar graphs are more qualitative, and, therefore, display categorical data. The figure below shows 1 bar graph (on the top) and 1 histogram (on the bottom):

Let’s look at an example of **double bar graphs**.

#### Example A

Kerry-Sue is surveying a random sample of students to determine which sports they would like to have set up at the end-of-year Safe Grad event. She collects the following data:

Sports |
Girls |
Boys |
---|---|---|

Racquetball | 6 | 3 |

Basketball | 3 | 6 |

Volleyball | 5 | 5 |

Swimming | 7 | 8 |

Draw a double bar graph and help Kerry-Sue determine which 2 sports would be most equally-liked by both boys and girls at the end-of-year Safe Grad event.

The double bar graph is as follows:

According to the double bar graph, volleyball and swimming seem to be almost equally liked by both the girls and the boys. Therefore, these 2 sports would be the ones Kerry-Sue should choose to set up at the end-of-year Safe Grad event.

#### Example B

Mrs. Smith teaches both academic and advanced math. She has been teaching these 2 courses for the past 4 years. She decided she wanted to compare her grades to see how each class was doing over the past few years and see if she has improved her class instruction at all. Her data can be found below:

Marks |
Academic Math |
Advanced Math |
---|---|---|

2007 | 61.3 | 74.7 |

2008 | 67.9 | 80.3 |

2009 | 50.9 | 86.8 |

2010 | 63.7 | 81.5 |

Draw a double bar graph and help Mrs. Smith determine if her class instruction has improved over the past 4 years.

The double bar graph is as follows:

Both the academic and advanced math marks went up and down over the past 4 years. If Mrs. Smith looks at the difference between 2007 and 2010, she can see that there is an improvement in the final grades for her students. Although there are many factors that can affect these grades, she can say that the change in her instruction is making some difference in the results for her students. Other factors might have contributed to the huge decline in grades for the academic math students in 2009. You can make this conclusion for Mrs. Smith, as there was a marked improvement in her advanced math course. In 2009, it seemed her instruction methods were working well with the advanced students, but other factors were affecting the academic students.

#### Example C

Robbie is in charge of the student organization for new food selections in the cafeteria. He designed a survey to determine if 4 new food options would be good to put on the menu. The results are shown below:

Food Option |
Yes votes |
No votes |
---|---|---|

Fish burgers | 10 | 5 |

Vegetarian pizza | 7 | 18 |

Brown rice | 23 | 9 |

Carrot soup | 20 | 20 |

Draw a double bar graph to represent the data, and draw any conclusions that you can from the resulting chart.

The double bar graph is as follows:

Robbie is trying to find out if any of the 4 food options would be desirable for the cafeteria menu. Using his survey results and plotting the yes votes versus no votes on a double bar graph, he should be able to quickly see that fish burgers and brown rice would be good choices for new items on the menu. Although many students did vote for carrot soup, the same number did not. Therefore, it would be a gamble to place this item on the new menu. Vegetarian pizza received more no votes than yes votes, so Robbie should not place this item on the menu.

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### Guided Practice

The grade 12 biology class did a survey to see what color eyes their classmates had and if there was a connection between eye color and sex. The following data was recorded:

Eye color |
Males |
Females |
---|---|---|

Blue | 5 | 5 |

Green | 6 | 8 |

Brown | 3 | 4 |

Hazel | 4 | 3 |

Draw a double bar graph to represent the data, and draw any conclusions that you can from the resulting chart.

**Answer:**

The double bar graph is as follows:

Eye color is an inherited trait. This means that the color of your eyes depends on both your mother and your father. Both the girls and boys groups have similar numbers for each of the 4 eye colors. If you look at the difference between boys and girls, you can see that there are more girls with green and brown eye colors and fewer girls with hazel eyes. The number of girls with blue eyes equals the number of boys with blue eyes, so there is no difference with regard to sex in this case. If you were to look at sex differences for the eye colors, the most observable difference can be found with green eyes. Green eyes are usually the least common of all the eye colors, but they are the most common here, so this may be significant, but it is hard to say from this chart.

### Explore More

The double bar graph below shows the numbers of dogs and cats adopted at a local animal shelter for each of the 4 quarters of last year. Use the double bar graph to answer the following questions:

- During which quarters of last year were more dogs adopted than cats?
- During which quarters of last year were more cats adopted than dogs?
- In total, how many dogs were adopted last year? How many cats were adopted last year?

The double bar graph below shows the numbers of cars sold by 2 used car dealerships for each day of last week. Use the double bar graph to answer the following questions:

- On what day did Dealership A and Dealership B combine to sell the most cars?
- How many more cars did Dealership B sell on Monday than Dealership A?
- On what day was there the biggest difference between cars sold by the 2 dealerships?

20 college graduates and 20 non-college graduates were asked their primary way of following the news, and the results are shown in the double bar graph below. Use the double bar graph to answer the following questions:

- How many more of the non-college graduates primarily use television to follow the news than use the newspaper?
- When college graduates and non-college graduates are combined, which form of the media is primarily used the least to follow the news?
- What percentage of the college graduates primarily use the internet to follow the news?

- The guidance counselor at USA High School wanted to know what future plans the graduating class had. She took a survey to determine the intended plans for both boys and girls in the school’s graduating class. The following data was recorded:

Future Plans |
Boys |
Girls |
---|---|---|

University | 35 | 40 |

College | 27 | 22 |

Military | 23 | 9 |

Employment | 10 | 5 |

Other/unsure | 5 | 10 |

Draw a double bar graph to represent the data, and draw any conclusions that you can from the resulting chart.