You and your five friends have been saving money for a special trip. Bill has saved $585, Susan has saved $785, Amanda has saved $623, Julie has saved $95, Roberto has saved $897, and you've saved $675. How can you represent what you've saved for your trip on a graph?
Watch This
First watch this video to learn about bar graphs
CK-12 Foundation: Chapter7BarGraphsA
Then watch this video to see some examples.
CK-12 Foundation: Chapter7BarGraphsB
Guidance
The different types of graphs that you have seen so far are plots to use with quantitative variables. A qualitative variable can be plotted using a 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. There is 1 bar for each category, with space between each bar, and the data that is plotted is discrete data. Each category is represented by intervals of the same width. When constructing a bar graph, the category is usually placed on the horizontal axis, and the frequency is usually placed on the vertical axis. These values can be reversed if the bar graph has horizontal bars. If bar graphs are constructed on grid paper, it is very easy to keep the intervals the same size and to keep the bars evenly spaced. In addition to helping in the appearance of the graph, grid paper also enables you to more accurately determine the frequency of each class.
Example A
Construct a bar graph to represent the depth of the Great Lakes:
Lake Superior – 1,333 ft.
Lake Michigan – 923 ft.
Lake Huron – 750 ft.
Lake Ontario – 802 ft.
Lake Erie – 210 ft.
The bar graph would appear as follows:
Example B
A questionnaire on the makes of people's vehicles showed the following responses from 30 participants. Construct a frequency distribution and a bar graph to represent the
data.
(F = Ford, H = Honda, V = Volkswagen, M = Mazda)
\begin{align*}& F \quad M \quad M \quad M \quad V \quad M \quad F \quad M \quad F \quad V \quad H \quad H \quad F \quad V \quad F\\ & H \quad H \quad F \quad M \quad M \quad V \quad H \quad M \quad V \quad V \quad F \quad V \quad H \quad M \quad F\end{align*}
The frequency distribution and bar graph can be constructed as follows:
Make of Car | Number of Cars |
---|---|
Ford | 8 |
Honda | 6 |
Volkswagen | 7 |
Mazda | 9 |
Example C
The following bar graph represents the results of a survey to determine the type of TV shows watched by high school students:
Use the bar graph to answer the following questions:
a. What type of show is watched the most?
b. What type of show is watched the least?
c. Approximately how many students participated in the survey?
d. Does the graph show the differences between the preferences of males and females?
Answers:
a. Sit-coms are watched the most.
b. Quiz shows are watched the least.
c. Approximately \begin{align*}45+20+18+6+35+16 = 140\end{align*} students participated in the survey.
d. No, the graph does not show the differences between the preferences of males and females.
Guided Practice
The following bar graph represents the part-time jobs held by a group of grade 10 students:
Using the above bar graph, answer the following questions:
a. What was the most popular part-time job?
b. What was the part-time job held by the least number of students?
c. Which part-time jobs employed 10 or more of the students?
d. Is it possible to create a table of values for the bar graph? If so, construct the table of values.
e. What percentage of the students worked as a delivery person?
Answer:
a. The most popular part-time job was in the fast food industry.
b. The part-time job of tutoring was the one held by the least number of students.
c. The part-time jobs that employed 10 or more students were in the fast food, delivery, lawn maintenance, and grocery store businesses.
d. Yes, it's possible to create a table of values for the bar graph.
Part-Time Job | Baby Sitting | Fast Food | Delivery | Lawn Care | Grocery Store | Tutoring |
---|---|---|---|---|---|---|
Number of Students | 8 | 14 | 12 | 10 | 13 | 5 |
e. The percentage of the students who worked as a delivery person was approximately 19.4%.
Practice
The bar graph below represents the amount of money that 7 people have in the bank. Use the bar graph to answer the following questions:
- Who has the most money in the bank?
- Who has the least money in the bank?
- How many of the above people have less than $800 in the bank?
The bar graph below represents the results of a survey in which tourists were asked which country they would most like to visit. Use the bar graph of answer the following questions:
- Which country would the tourists most like to visit?
- Which country would the tourists least like to visit?
- How many countries were the most desired destination for more than 25 tourists?
The bar graph below represents the results of a survey in which students were asked their favorite superhero. Use the bar graph to answer the following questions:
- Who was the most popular superhero?
- Who was the least popular superhero?
- How many students had a favorite superhero of Wonder Woman?
- What percentage of the students had a favorite superhero of Wonder Woman?