Hello, and welcome to this video about line graphs!
Today we’ll explore what a line graph is and what type of data it’s used to represent.
We’ll also learn how to use line graphs to interpret situations in the real world.
Before we get started, let’s review a few things.
First, a graph is a diagram that shows the relationship between two quantities, which we call variables.
These variables are measured along the x-axis and y-axis on a coordinate plane.
A line graph is a type of graph that displays quantitative data as a series of points called markers or data points.
These data points are connected by straight line segments.
The connected data points show the relationship between two variables.
A line graph is typically used to show information that changes over time.
Let’s take a look at an example.
This line graph shows the change in a company’s profits over several years.
The x-axis is labeled “Year,” and the y-axis is labeled “Profits.”
We see that line segments connect the data points plotted on the graph.
Since the line segments are generally moving in a positive direction, we can say that the company’s profits tended to increase from 2006 to 2013.
Let’s take a look at the line segment connecting the data points for the years 2009 and 2010.
We can see that this particular line segment is positioned in a downward or negative direction.
This tells us that the company’s profits decreased from 2009 to 2010.
What do you notice about the line segment connecting the data points for 2012 and 2013?
They form a straight horizontal line.
This shows that the company’s profits neither increased nor decreased during this timeframe.
Instead, they stayed the same.
When constructing a line graph on a coordinate plane, the x-axis is always used to plot the independent variable, and the y-axis is always used to plot the dependent variable.
With line graphs, the independent variable is usually time.
In the graph we just looked at, the independent variable is “years,” which is a measurement of time.
The dependent variable is the factor that changes over time.
In our example, the dependent variable is the company’s profits, which increased and decreased from 2006 to 2013.
Line graphs are an important part of our everyday lives because they can swiftly communicate data and trends.
They’re used in a wide variety of fields, including Sales and Marketing, Science, Psychology, Economics, and Business.
Additionally, line graphs can be used to make predictions.
Let’s look once more at our line graph showing the company’s change in profits.
Based on the general trend shown, do you think profits will increase or decrease in the future?
We can infer that profits may continue to increase based on the positive trend shown in previous years.
Let’s look at another line graph together.
This graph shows how much time Dave spent playing video games each day.
The horizontal x-axis shows the independent variable, which is “Days.”
And the vertical y-axis shows the dependent variable, which is “Minutes Spent Playing Games.”
Each marker shows the data point for how many minutes of video games Dave plays each day.
Let’s use this information to answer some questions.
Which day did Dave spend the most time playing video games?
Dave spent the most time playing video games on Day 4.
We know this because the marker for Day 4 is higher than the markers for the rest of the days shown.
On Day 4, Dave played games for 100 minutes.
That’s a lot of gaming!
What is the difference in the amount of time Dave spent playing video games on Day 2 and Day 6?
Looking at the markers, the graph shows that Dave played games for 70 minutes on Day 2 and 90 minutes on Day 6.
The difference is calculated by subtracting.
Since 90 minus 70 equals 20, the difference is 20 minutes.
Dave spent 20 more minutes playing video games on Day 6.
How many minutes did Dave play video games altogether?
To find the total amount of time Dave played video games, add the amount of minutes played each day:
30 plus 70 plus 60 plus 100 plus 10 plus 90, equals 360.
Therefore, Dave spent 360 minutes playing games from Day 1 through Day 6.
A line graph can show multiple sets of data if the same two variables are related.
Graphing multiple data sets on a line graph can be very informative because they can be compared and contrasted.
When this happens, each data set is typically represented by a distinct color.
The line graph contains a key that explains what data set each color stands for.
Let’s take a look at a line graph that shows two sets of data.
This graph shows how much money was raised in a school fundraiser each month.
The horizontal x-axis shows the independent variable, which is “Month.”
And the vertical y-axis shows the dependent variable, which is “Amount raised.”
Each marker shows the data point for how much money was raised in each month shown.
The 2 data sets are graphed in 2 different colors, blue and green.
By reading the key beneath the graph, we see that green represents money raised by seventh-grade students and blue represents money raised by eighth-grade students.
Let’s use this information to answer some questions.
Pause the video after the question is asked.
Then, look at the graph and see if you can answer it yourself.
When you’re ready, resume and check your work.
Which grade raised more money in September?
Eighth-grade students raised more money than seventh-grade students in September.
Remember that blue data points represent eighth-grade students and green data points represent seventh-grade students.
Looking at the markers for September, we see that the blue marker is higher than the green marker, so eighth-grade students raised more money in September.
Which grade raised more money in the months of June and August combined?
The eighth-grade students (shown in blue) raised 60 dollars in June and 60 dollars in August.
60 plus 60 equals 120, so the eighth-grade students raised 120 dollars in June and August.
The seventh-grade students (shown in green) raised 20 dollars in June and 100 dollars in August.
20 plus 100 equals 120, so the seventh-grade students raised 120 dollars in June and August.
As you can see, both grades raised the same amount of money in the months of June and August combined.
In which month did eighth-grade students raise the smallest amount of money?
How much money was raised?
We can find the answer by examining the blue markers representing the eighth-grade data points in each month.
The month that the marker is placed the lowest is in May when they raised 40 dollars.
I have one last graph for you to analyze.
This one is a little more challenging, but I know you can handle it.
As you can see, this line graph displays 3 sets of data.
Consider the following questions:
Which variable is independent?
Which is dependent?
Explain.
In which month was the number of computers sold in Shop C almost identical to the number sold in Shop B?
In which months did Shop A sell more computers than Shops B or C?
Pause this video, analyze the line graph, and see if you can answer these questions yourself.
When you’re ready, resume the video and we’ll go over the answers together.
Now that you’ve tried these problems yourself, let’s go over them together.
Which variable is independent?
Which is dependent?
Explain.
The independent variable is “Months,” which is on the x-axis.
The independent variable is always measured along the x-axis, and it usually pertains to time.
In this case, time is measured in months.
The dependent variable is “Number of Computers Sold,” which is on the y-axis.
The value of the dependent variable relies on the independent variable.
In this case, the number of computers each store sold depends on the month.
In which month was the number of computers sold in Shop C almost identical to the number sold in Shop B?
March.
When we look at the markers for that month, we see that the red marker for Shop B and the green marker for Shop C almost overlap entirely.
This indicates that the number of computers sold by each shop was about the same.
In which months did Shop A sell more computers than Shops B or C?
February and March.
To find out when Shop A sold the most, look for when the blue markers are higher than the green or red markers.
Shop A sold 40 computers in February and 50 computers in March.
Line graphs are useful tools for showing how factors change over time.
I hope this video about line graphs was helpful.
Thanks for watching, and happy studying!