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Line Graphs

Display given data as linear change on coordinate graphs.

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Line Graphs

Let's Think About It

License: CC BY-NC 3.0

For Jose's economics class he wants make a graph that illustrates the number of persons employed in the U.S. who were 16 years and older in 2011. He has organized his data into the following table.

Jose's Data
Month Num. of People
Jan 153250
Feb 153302
Mar 153392
Apr 153420
May 153700
Jun 153409
Jul 153358
Aug 153674
Sep 154004
Oct 154057
Nov 153937
Dec 153887

How can Jose make a graph to illustrate the data over time? 

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

Guidance

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 line graphs.

One way to display data is in a line graph. A line graph shows the relationship between independent and dependent values of data, and are usually used to show trends over time. In the graph each data value is represented by a point in the graph that are connected by a line. The independent variable is listed along the horizontal, or x, axis and the quantity or value of the data is listed along the vertical, or y, axis. 

Let's look at an example.

Kelsey works at an arboretum and tracks tree growth over time. Kelsey collected the growth data of one tree over five years and organized her data into the table below. Create a line graph that represents the data over time. Then state two conclusions about the data.

Year Size of Tree (in feet)
2003 2
2004 2.5
2005 3.5
2006 8.5
2007 14

First, create the line graph. To do this, draw the horizontal (x) and vertical (y) axes. 

License: CC BY-NC 3.0

Next, label the vertical axis. The vertical axis lists the dependent variable and represents the quantity of the data. In this case, the dependent variable is feet and the label will also be "feet."

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 “Tree Growth.”

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 2 and the largest is 14. Based on these values label the vertical axis from 0-16. Since the values are whole numbers and are relatively spread out, 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 data points. To do this, write the years along the horizontal axis, leaving space between each. Each year will have one point representing the height of the tree. To start, draw a point for the the height in 2003. To do this find 2003 on the horizontal axis and go up until 2, then draw a point. Then draw the point for the height in 2004. Continue drawing the points for all the years.  

Next, draw the line. To do this, start with the point on the far left of the graph and connect the points with one line from 2003 to 2007. 

Then, state two conclusions from the graph. To do this, analyze the graph by comparing the steepness of the line between each point. 

The first answer is the graph should look like the one below. The second answer is two conclusions that can be made from the graph are: the greatest amount of growth occurred between 2006 and 2007 and from 2005 to 2006 the tree's height more than doubled. 

License: CC BY-NC 3.0

Guided Practice

The line graph below shows the temperature over seven days in July in Missouri. List two conclusions that can be made from the graph.

License: CC BY-NC 3.0

First, analyze the graph by comparing the shape of the line between the points.

The answer is two conclusions can be made from the graph: three dates, July 20-22, all had the same temperature of 86 degrees and the temperature is rising from July 22 to July 24.

Examples

Example 1

The population for the city of Los Angeles is organized in the table below. Create a line graph to that represents the population change over time. Then state one conclusion about the data. 

Year: Approximate Population (in millions):
1950 2
1960 2.5
1970 2.8
1980 3
1990 3.5
2000 3.7

First, make the line 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 independent variable. In this case, the independent variable is the year and the axis will be labeled "Year."  

Next, label the vertical axis. The vertical axis lists the dependent variable and represents the quantity of the data. In this case, the dependent variable is the population and the label will be "Population (in millions)."

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 “Population of Los Angeles (in millions).”

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 2 and the largest is 3.7. Based on these values label the vertical axis from 0-4. Since the values include decimals and are relatively close, a unit of 0.5 can be used. Therefore, the vertical axis will start at 0 and go to 4 by increments of 0.5.

Next, draw the data points. To do this, write the years along the horizontal axis, leaving space between each. Each year will have one point representing the population. To start, draw a point for the the population in 1950. To do this find 1950 on the horizontal axis and go up until 2, then draw a point. Next, draw the point for the population in 1960. Continue this pattern for all the years.  

Next, draw the line. To do this, start with the point on the far left of the graph and connect the points with one line from 1950 to 2000. 

Then, state one conclusion from the graph. To do this, analyze the graph by comparing the steepness of the line between the points. 

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: the population of Los Angeles has increased from the years 1950 to 2000 and it is estimated that it will continue to increase for the future.   

License: CC BY-NC 3.0

Example 2 

The Electronic Energies Alliance recorded the average cost of one gallon of gasoline in the United States for the years 2000-2007. The graph below represents their data. List three statements about the data. 

License: CC BY-NC 3.0

First, analyze the graph by comparing the shape of the line. 

The answer is three statements can be made about the graph: there was a drop in the price of gas from 2000 to 2001 and again from 2006 to 2007, the price of gas increased from the years 2001 to 2006, and the price of gas increased the most from 2005 to 2006.

Example 3

The graph below illustrates the absolute minimum temperature in Dubai in 2005 in celsius. List two statements that can be made about the data. 

License: CC BY-NC 3.0

First, analyze the graph by comparing the shape of the line.

The answer is two statements can be made about the graph: the greatest minimum temperature occurred in September and was approximately 31 degrees celsius, and the absolute minimum temperatures increased from the months of February to September.

Follow Up

License: CC BY-NC 3.0

Remember Jose and his economics class? 

Jose needs to create a graph that illustrates the number of people employed in the U.S. who were 16 years or older in 2011. Jose's data is presented in the table below. 

Jose's Data
Month Num. of People
Jan 153250
Feb 153302
Mar 153392
Apr 153420
May 153700
Jun 153409
Jul 153358
Aug 153674
Sep 154004
Oct 154057
Nov 153937
Dec 153887

First, 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 independent variable. In this case, the independent variable is the month and the axis will be labeled "Month."  

Next, label the vertical axis. The vertical axis lists the dependent variable and represents the quantity of the data. In this case, the dependent variable is the number of persons employed and the label will be "Number of Persons."

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 “Number of Persons Employed in the U.S. Aged 16+ Years in 2011.”

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 153250 and the largest is 154057. Based on these values label the vertical axis from 153000 to 154250. Since the values are whole numbers and are relatively close, a unit of 250 can be used. Therefore, the vertical axis will start at 153000 and go to 154250 by increments of 250.

Next, draw the data points. To do this, write the months along the horizontal axis, leaving space between each. Each month will have one point representing the number of people employed. To start, draw a point for the number of people employed in January. To do this find January on the horizontal axis and go up until 153250, then draw a point. Next, draw the point for the people employed in February. Continue this pattern for all months.  

Next, draw the line. To do this, start with the point on the far left of the graph and connect the points with one line from January to December. 

The graph should look like the one below. 

License: CC BY-NC 3.0

Video Review

Explore More

Use this line graph to answer the following questions.

The vertical axis shows the number of vegetables harvested each year. This is recorded as vegetable growth. The horizontal axis shows the years vegetable growth was recorded.

1. How many vegetables were harvested in 2005?

2. How many vegetables were harvested in 2006?

3. What is the difference in growth from 2005 to 2006?

4. How many vegetables were harvested in 2007?

5. What is the difference in vegetable growth from 2006 to 2007?

6. What is the vegetable growth in 2008?

7. What is the difference in vegetable growth from 2005 to 2008?

8. If the vegetable growth follows the same pattern from 2008 to 2011, what will the new total be?

9. If there is a loss of 50 vegetables from 2008 to 2009, what will the new total be?

10. If there is a gain of 100 vegetables from 2008 to 2009, what will the new total be?

11. If there is a loss of 50% from 2008 to 2009, what will the new total be?

12. True or false. A bar graph shows the same data as a line graph?

13. True or false. A line graph must show how data changes over time.

14. - 15. Use a newspaper to find two line graphs. The business section is a good place to start. Examine the data and explain what the line graph represents to a friend.

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 11.7. 

Vocabulary

bar chart

bar chart

A bar chart is a graphic display of categorical variables that uses bars to represent the frequency of the count in each category.
broken line graph

broken line graph

A broken line graph is a graph that is used to show changes over time. A line is used to join the values but the line has no defined slope.
continuous variables

continuous variables

A continuous variable is a variable that takes on any value within the limits of the variable.
data set

data set

A collection of these observations of the variable is a data set.
dependent variable

dependent variable

The dependent variable is the output variable in an equation or function, commonly represented by y or f(x).
discrete random variables

discrete random variables

Discrete random variables represent the number of distinct values that can be counted of an event.
independent variable

independent variable

The independent variable is the input variable in an equation or function, commonly represented by x.
Line Graph

Line Graph

A line graph is a visual way to show how data changes over time.
qualitative variable

qualitative variable

A qualitative variable is one that cannot be measured numerically but can be placed in a category.
quantitative variable

quantitative variable

A quantitative variable is a variable that takes on numerical values that represent a measurable quantity. Examples of quantitative variables are the height of students or the population of a city.
variable

variable

In statistics, a variable is simply a characteristic that is being studied.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
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  9. [9]^ License: CC BY-NC 3.0

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