Line Plots
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Learning text on the topic Line Plots
Line Plots – Definition
In mathematics, we have lots of different types of graphs, which represent data in many different ways. You may be familiar with; bar charts, pie charts, scatter graphs and others. When you know more about maths, the more graphs you will recognise. In this learning text, we are going to learn about line plots.
A line plot is a graph that displays data along a number line. It is a simple way to represent data by placing small marks, such as marks above the number line to show the frequency of the data.
Creating and Analysing Line Plots – Steps
Line plots can be created using just a data set and a number line that represents the items in your data set. In order to use the line plots effectively and then answer some questions about the data set, you need to follow these steps:
- Create a data set using the given data. Organise your data set and sort the data.
- Create a number line with the range of numbers in the data set (from lowest to highest). This number line will be the foundation of your line plot.
- Represent the amount of each item from the range of your data set with one mark on the line plot.
- Assign a title to your line plot once your data set is completely displayed on the line plot.
The line plot can now be used to interpret the data set and answer questions about the data set.
Creating Line Plots – Example
Let’s look at the example below and then use our knowledge to answer some questions about the data.
From our bunch of data sets (the picture below) we can create a line plot. Let’s look at the steps carefully. Line plots are very helpful as they help visualise our data set in a very organised way.
Our data set is an unsorted amount of honey jars. On top of that, the jars are filled with different amounts of honey. All we have to start with is a recording of all the jars filled with different amounts of honey.
Now we need to organise and categorise this data to be more comprehensible.
Firstly, we must organise the data sets in order, from smaller to larger numbers. We have zero two times, the $\frac{1}{4}$ appears four times, $\frac{1}{2}$ comes up five times, $\frac{3}{4}$ turns up four times and finally number one accrue three times.
| Data Set |
|---|
| 0 0 |
| 1/4 1/4 1/4 1/4 |
| 1/2 1/2 1/2 1/2 1/2 |
| 3/4 3/4 3/4 3/4 |
| 1 1 1 |
After we put our data in order, we can draw a number line which will include all of the numbers from our data set from least to greatest. Make sure there is an equal distance between the numbers, this is called a scale. We must also remember to label our line plot.
Since our number line represents different amounts of honey in a certain number of jars, we call this line plot The level of honey in jars.
The next step is to use our data set and plot the information on the number line.
Firstly, we put two ($2$) marks above zero ($0$) on our number line because there were two jars without any honey in them. We must make sure the marks are the same size and equal distance from each other. We’ll do the same with the rest of the data. We plot four marks above one-quarter ($\frac{1}{4}$), five marks above a half ($\frac{1}{2}$), four marks above three quarters ($\frac{3}{4}$) and three marks above full jars ($1$).
Have a look at the finished graph below.
The last thing to do now is to find a title for the graph. We’ll call it Sticky Fingers Inventory because it comes from Nari’s company which is called “Sticky Fingers Honey Company”.
Interpreting Line Plots – Tips and Tricks
We can use line plots in mathematics and statistics for various reasons. For example, to show exact values from the data set, or to show the relationships between items in our data set. We can also use line plots to visualise a data set or to compare and analyse two or more data sets.
Using our example from above, we can now look at our set of data in an organised way on the line plot we created and answer questions about the data set. Answering questions about a data set is a part of analysing and interpreting data.
Let’s look at some questions about the data we have displayed on the line plot above. The line plot is a simple visual representation of the data. We can use it to analyse, interpret and evaluate the data from our data set by comparing the height of the columns.
Let’s take a look at some questions about our sticky fingers inventory:
Most of the jars are filled half way.This is shown visually by the tallest line on the graph at $\frac{1}{2}$ levels of honey.
There are four jars in one quarter and four jars in three quarters levels of honey in a jar.
There are three full jars and two empty jars. So we can say that there is one more full jar in the inventory.
There are a total of sixteen jars, we exclude the empty jars because they would not be for sale.Line Plots – Summary
Let’s summarise what we learned about line plots today.
The purpose of a line plot is to show data in an organised way so we can understand it better and be able to answer questions about the information which the line plot represents. We can plot the data by putting marks on the number line that represent an element from our data set. Remember to label the units of measurement for the line plot as well as giving your line plot a title, making sure the title is related to the information the graph represents.
Take a look at the overview chart below explaining the necessary steps to creating a line plot:
| Step # | What to do |
|---|---|
| 1 | Collect your data or use the given data set. |
| 2 | Organise the data sets in order, from smaller items to larger ones. |
| 3 | Draw a number line which will include all the numbers from your data set from least to greatest. |
| 4 | Plot the data by putting marks or dots above the measurement on the number line. |
| 5 | Label the units of measurement for the line plot. |
| 6 | Find a fitting title that is related to the information the graph represents. |
Now you should be able to collect, analyse and interpret data on the line plot and answer specific questions related to the same data if necessary. For more, check out fractions on line plots.
Frequently Asked Questions about Line Plots
Line Plots exercise
-
Can you order the fractions?
HintsWhat number goes at the beginning of the number line? What number goes at the end?
Look at the fractions provided. What is the smallest fraction? What is the largest?
Which fraction should be in the middle of the line plot diagram? Which fraction shows one-half?
SolutionThe fractions in order from least to greatest is 0, $\frac{1}{6}$, $\frac{2}{6}$, $\frac{1}{2}$, $\frac{4}{6}$, $\frac{5}{6}$, 1.
Remember, least means smallest and greatest means biggest. -
Parts of a line plot diagram.
HintsThe data represented here are fractions, but what is the proper name for a group of data?
The units of measurement are what we are measuring in the line plot.
SolutionThe data set is a list that groups like amounts together. Here, our data set is fractions.
The number line includes all the numbers from our data set in order from least to greatest.
The units of measurement label used for the number line names the type of data in the data set.
The title tells us what information we will learn from these line plots. We learn about Nari’s honey jar sales, so the title is Sticky Finger's Honey Pot Sales. -
Use the line plot diagram to answer the questions.
HintsTo find out how many of an amount are filled, count the 'x's above the fraction. For example, there are 2 jars that are $\frac{5}{6}$ filled.
To find the quantity with the most number of jars, find the fraction with the most 'x's.
To find the quantity with the least number of jars, find the fraction with the least 'x's.
If the question asks how many more or how many fewer, think about what equation will help you solve this.
If the question asks you to combine two amounts, you need to add.
Solution1.) How many jars are $\frac{1}{2}$ filled? 3.
- There are 3 'x's above the fraction $\frac{1}{2}$ on the number line showing that 3 of the jars are half filled.
- This is the most amount of jars in his inventory.
- This is the least amount of jars in his inventory.
- There are 4 jars that are $\frac{4}{6}$ filled and 2 jars that are full. 4 - 2 = 2.
- There are 4 jars that are $\frac{4}{6}$ filled and 3 jars that are $\frac{1}{2}$ filled. 4 + 3 = 7.
-
Interpreting a line plot diagram.
HintsLook at line plot diagram, the amount of 'x's are different for each day of the week. Each x represents 1 jar of honey.
To find the day with the most number of honey sales, find the day with the most 'x's above it.
To find the day with the least number of honey sales, find the day with the least number of 'x's above it.
If the question asks you to combine two amounts, you need to add.
SolutionThe correct statements are:
- The least amount of honey was sold on Thursday. On Thursday Nari sold 1 jar of honey - this is the smallest amount of honey sold during the week.
- Nari sold the same amount of honey on Monday and Friday. Nari sold 5 jars of honey on Monday and 5 jars of honey on Friday.
- On Thursday and Friday, Nari sold 6 jars of honey. On Thursday, Nari sold 1 jar of honey. On Friday, Nari sold 5 jars of honey. 1 + 5 = 6.
- Twice as many jars of honey were sold on Wednesday than on Tuesday. On Wednesday, 6 jars of honey were sold. On Tuesday, he sold 3. 3 x 2 = 6.
These statements are incorrect:
- Nari sold the most amount of honey on Tuesday. Nari sold the greatest amount of honey on Wednesday.
- Nari sold a total of 19 jars of honey during the week. Count and add the 'x's from the line plot diagram carefully! 5 + 3 + 6 + 1 + 5 = 20.
-
Which line plot diagram represents the data in the table?
HintsEach x represents a jar.
There are 8 jars with no honey in them so the correct line plot has 8 'x's above 0.
SolutionEach x represents one type of honey jar.
8 of the jars have zero honey in them.
4 of the jars are $\frac{1}{4}$ full of honey.
3 of the jars are $\frac{1}{2}$ full of honey.
7 of the jars are $\frac{3}{4}$ full of honey.
2 of the jars are completely full of honey. -
How many jars of honey does Nari have to sell?
HintsEach x represents 1 jar of honey.
Should Nari count the empty jars of honey?
SolutionTo solve this problem, you need add up all of the 'x's above one-sixth, two-sixth, one half, four-sixth, five-sixth and one whole.
Nari has 15 jars of honey.
3 + 1 + 3 + 4 + 1 + 3 = 15
Why did we not count the 'x's above the zero? Nari would not sell empty jars!
