Katie is a member of the Young Entrepreneurs and she must present a proposal for a summer job. She decides to operate an ice cream stand during summer vacation. If her proposal is chose as the one “most likely to succeed” then her startup costs will be covered by the Young Entrepreneurs. Katie begins by asking people to name their favorite ice cream flavor.

The results of her survey are displayed on the following bar graph.

What information can Katie present to the Young Entrepreneurs from this graph? If the ice cream freezer holds ten gallons of ice cream, how can the chart help Katie when she has to place her first order?

In this concept, you will learn how to recognize and interpret the data displayed on a bar graph.

### Bar Graphs

In the real world, you are expose to data every day. If you watch the weather forecast on TV you are presented with information about the weather for the day as well as information about the weather for the entire week ahead. When you receive your report card you are given data about your marks and your attendance.

**Data** is simply collected information. This information often takes the form of a collection of numbers which can be visually displayed in a table or on a graph.

When you conduct a survey, measure how changes occur over time or study changes in trends, the recorded information is data. The data should be analyzed, organized and visually displayed. One type of visual display is a bar graph.

A bar graph is probably the type of graph that you have worked with most often over the years. Do you remember what a bar graph is and what purpose it serves as a visual display of information?

A **bar graph** is a visual way of showing information in which quantities corresponding to particular categories are represented by rectangular bars of equal width. The lengths or heights of the rectangular bars compare the quantities in different categories.

If you are going to display your recorded data using a bar graph then the graph must have a title clearly stating what the graph is about. One axis of the chart must be labeled so as to show the categories being compared and the other axis must have a label and a suitable scale to represent the quantity being displayed. A bar graph can have either vertical bars or horizontal bars.

Below is a bar graph representing the average monthly rainfall in the capital city for the first six months of the year 2014.

In the above bar graph the title is clearly shown above the graph and both axes are labeled. The vertical bars compare the average amount of rainfall for each of the six months. This same bar graph can also be displayed using horizontal bars as shown below.

Remember that a bar graph displays collected data and this data can lead you to discussions and allow you to draw conclusions. Let’s use the above bar graph to answer some questions.

In which month did the most amount of rain fall?

First, look at the horizontal bars on the graph and find the longest bar. The longest bar is the one that extends farthest to the right.

Then, look to the left of this longest bar to see the month represented by this bar.

The answer is May.

What was the average rainfall for the month of February?

First, look on the vertical axis and find the month of February.

Next, follow the horizontal bar for this month to the right until you reach the end of the bar.

Then, find the value on the horizontal axis labeled ‘Rainfall (mm)’ that corresponds with the end of the bar.

The answer is 65 mm.

Which month had the lowest average rainfall?

First, look at the horizontal bars on the graph and find the shortest bar. The shortest bar is the one that extends least to the right.

Then, look to the left of this longest bar to see the month represented by this bar.

The answer is June.

### Examples

#### Example 1

Earlier, you were given a problem about Katie and her presentation to the Young Entrepreneurs.

The tallest vertical bar is above ‘Bubble Gum’ ice cream and it is the favorite flavor. The second tallest bar is the vertical bar above ‘Cotton Candy’ and it is the second favorite flavor. She should order three gallons of each of these flavors. The third tallest vertical bar is the one above ‘Hoof Prints’. She should order two gallons of this flavor. The last two flavors of ‘Chocolate’ and ‘Vanilla

are the least favorite flavors so one gallon of each of these should be ordered.#### Example 2

Use the bar graph below to answer the questions presented below the graph.

The bar graph below compares the lunch options available in the school cafeteria to the number sold during one week.

Which item was purchased the least from the cafeteria?

First, look at the vertical bars on the graph and find the shortest bar. The shortest bar indicates the item that was bought the least.

Next, look below this bar and find the name of the item represented by this bar.

The answer is Caesar Salad.

The Daily Special is always available in the cafeteria. The remaining items will only remain on the menu if 75 or more of that item are sold. Which items will remain on the menu?

First, look at the vertical bars on the graph and find the numbers above each bar. This number represents the number of sales for the item.

Next, find all the bars that have a top number equal to or greater than 75.

The answer is Soup and Chicken Burger.

How many items were sold in the cafeteria altogether?

First, look at the vertical bars on the graph and record the numbers above each bar.

Then, calculate the sum of the numbers you have recorded.

The answer is 475.

#### Example 3

A bar graph is often drawn with two or more bars in each category. These bars compare same quantities in one category. The following bar graph displays the temperature in degrees Fahrenheit for the third week of May for the years 2000 and 2015 respectively. Use the bar graph to answer the questions presented below the graph.

What was the highest recorded temperature in the year 2000?

First, look at the bar graph to determine which color bar represents the year 2000.

Next, look at the temperatures above each bar for the year 2000 and record the highest number.

The answer is 70 degrees Fahrenheit.

What is the lowest temperature recorded for the year 2015?

First, look at the bar graph to determine which color bar represents the year 2015.

Next, look at the temperatures above each bar for the year 2015 and record the lowest number.

The answer is 60 degrees Fahrenheit.

What is the average daily temperature for the week displayed on the bar graph for each year?

First, begin with the year 2000 and record the seven temperatures displayed on the bar graph.

Next, calculate the sum of the recorded temperatures.

Then, divide the sum by the number of days to determine the average daily temperature.

The answer is 61.1 degrees Fahrenheit for the year 2000.

Next, repeat the steps for the year 2015.

The answer is 65.7 degrees Fahrenheit for the year 2015.

#### Example 4

The bar graph below compares the air travel costs to fly to various U.S. cities from Oakland, California on three different Airlines. Use the information displayed on the bar graph to answer the questions presented below the graph.

For which cities did all three Airlines have a similar price?

First, look at the tops of the bars. The numbers displayed represent the cost in US dollars charged by each of the Airlines to fly from Oakland, California to the city named below the vertical bars.

Next, subtract the lowest value displayed above the group of bars from the highest value to determine the range in US dollars between the costs of the three airlines. Remember to record your results.

The answer is Las Vegas and Atlanta.

Which Airline had the lowest price for three of the five cities?

First, look at the three vertical bars above each city. Record the value displayed above the shortest bar for each city.

Next, record the name of the airline that corresponds to the value above each of the shortest bars.

Next, determine which airline name appears most in your list.

Then, match the name of the city with the airline offering the lowest price.

The answer is Coast to Coast Airlines.

For which city did Western Airlines and Coast to Coast Airlines have a difference in price of forty dollars?

First, look at the three vertical bars above each city. Use the legend presented above the bar graph to find the vertical bars for Western Airline and Coast to Coast Airlines.

Next, record the cost values above these two vertical bars for travel to each of the cities.

Next, subtract the values to determine the difference in cost charged by each of the two airlines.

Then, match the difference of forty dollars with the corresponding city named below the bars.

The answer is Orlando.

### Review

The following bar graph compares the average price of gasoline in five US states. Use the information displayed in the graph to answer the questions that follow.

1. What was the average price of gasoline in Hawaii?

2. What was the average price in Florida?

3. Which state had the lowest average price per gallon?

4. Which state had the highest average cost per gallon?

5. If the average cost in Missouri is $3.00 per gallon, what would 15 gallons cost you in Missouri?

6. Would it be cheaper to buy ten gallons in Hawaii?

7. How much would it cost you to purchase the ten gallons in Hawaii?

8. If the average cost is $3.40 per gallon in California, what would be the difference between ten gallons in Hawaii and ten gallons in California?

9. What is the average price per gallon in Washington State?

10. Based on the bar graph, which state has a cheaper price per gallon, Florida or Washington?

The following bar graph shows how the number of teams participating in the Iditarod has changed over time. Use the information displayed in the bar graph to answer the questions presented below the graph.

11. About how many teams participated in 2006?

12. Which year had the highest participation?

13. If the number of teams in 2008 had doubled in 2010, how many teams would have participated in 2010?

14. True or false. There has been a steady increase in participation from 2007 to 2010.

15. If the participation in 2011 increased 10 mushers from the number counted in 2010, how many mushers would be participating?

16. True or false. There were less mushers participating in 2006 compared with 2007.

17. Which statement best describes the participation in 2009?

- It was better than in 2007.
- There were less than 80 mushers registered.
- It was the smallest number of mushers recorded on the graph.
- Both B and C.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 1.1.