What Is a Line Graph?
Line graphs form an essential part of statistics in mathematics. A line graph comprises points and line segments depicting the relationship between two datasets. A line graph describes the change in a quantity over time. For example, the variation in average daily temperatures over a week or a month can be represented using a line graph.
We can draw a line graph by plotting points on the coordinate plane. If the line graph for two data sets is a straight line then the graph is called a Linear Graph.
In some textbooks, a line graph is referred to as a line plot as well.
How Do We Draw a Line Graph?
For any given data sets, we can draw a line graph by following these steps:
Step 1: Write the ordered pairs from the data sets
Step 2: Select appropriate numbers for the two axes to depict the data set values on a coordinate plane
Step 3: Write a title for the graph and label the axes.
Step 4: Plot points for the ordered pairs and join them to form line segments.
How Do We Interpret a Line Graph?
We can interpret a line graph by observing the pattern and variation in data values of the plot. Let’s take a look at an example:
Here is a line plot depicting a cat’s weight over 5 months.
Now, if we want to find the age at which the cat gained the least and most weight, we can simply observe the variation in the line graph.
The maximum weight difference occurs between the points (3, 25) and (4, 40) and least weight difference occurs between the points (2, 20) and (3, 25).
So, the cat gained the maximum weight from the age of 3 months to 4 months and the least weight from the age of 2 months to 3 months.
Solved Examples
Example 1: The line graph shows the number of views for a video over 8 days.
a. How many views does the video have after 3 days?
b. What is the difference in the number of views on days 5 and day 6?
c. When does the video get the most number of views?
Solution:
From the graph:
a. Number of views after 3 days = 50 views
b. Number of views on day 5 = 125
Number of views on day 6 = 175
So, difference in number of views on day 5 and day 6 = 175 – 125
= 50 views
c. Look for the steepest line segment in the graph. The greatest increase in the number of views occurs from day 7 to day 8.
So, the video gets the most views from day 7 to day 8.
Example 2: Observe the line graph and answer the following questions.
a. In which month was Kathy’s savings $250?
b. When does Kathy’s savings remain constant?
Solution:
a. From the graph,
Kathy’s savings in July = $250
Kathy’s savings in September = $250
So, Kathy’s savings in July and September are 250$.
b. Observe the steepness of the line segments in the graph.
The graph is flat from January to February.
So, Kathy’s savings remained constant from January to February.
Example 3: The table shows the number of candy boxes sold across 5 days. Represent the data using a line graph.
Candy boxes Sold | 5 | 4 | 7 | 5 | 10 |
Day | Monday | Tuesday | Wednesday | Thursday | Friday |
Solution:
Represent the number of boxes sold on the y – axis. Since, the minimum number of boxes sold is 4 and the maximum number of boxes sold is 10, we can mark numbers 1 to 10 on the y – axis with an interval of 1. Label y-axis ‘Number of Candy Boxes’.
a. Represent the days on the x-axis. Label the x-axis as ‘Day’
b. Write Candy Boxes Sold as the title of the graph
c. Mark the points corresponding to 5 boxes sold on Monday, 4 boxes sold on Tuesday, 7 boxes sold on
Wednesday, 5 boxes sold on Thursday and 10 boxes sold on Friday.
d. Connect the points to form line segments.
Hence, the line graph is as given in the image:
A line graph is useful in determining the rate of change of one dataset with respect to a related dataset.
We can use bar graphs, pie charts and histograms to represent and interpret data.
Data is a value collected using measurements or observations.