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# Line Plots

As mathematicians, we can calculate all kinds of interesting numbers based on the world around us. But how do we communicate these numbers to other people? The best way to do this is by expressing our numbers in a visual, easy-to-understand format. And when it comes to visual tools, line plots represent an excellent option. Pretty much anyone can understand what numbers and statistics mean with one quick look at a line plot. But how do we build our own line plots?

## Line plots: An explanation

Different mathematicians use different names for line plots, and some call them "dot plots." But no matter what we decide to call it, a line plot is a type of graph. As the name "dot plot" suggests, these graphs display data visually using dots on a line. The number of dots corresponds to statistical values.

For example, you might ask your friends how many shoes they own. This quick survey might provide you with a range of different results. Five of your friends might own just one pair, three might own two pairs, and two might own five pairs.

Each of these values would give us a different number of dots on a line graph. We'd get five dots for one pair of shoes, three dots for two pairs of shoes, and two dots for five pairs of shoes.

## Building your own dot plot

Try building your own dot plot by conducting your own quick survey. Send out a few text messages and ask your friends how many shoes they own.

Next, all we need to do is draw a horizontal line with numbers along the bottom -- perhaps from 1 to 10.

Finally, take your data and write dots above each number based on how many of your friends have a certain number of shoes.

It's that easy!

## Interpreting line plots

Consider the following line plot:

What does this tell us about the number of students in each classroom?

We can see that one class has just 26 students, two classes have 27 students, four classes have 29 students, two classes have 30 students, one class has 31 students, no classroom has 32 students, and one class has 33 students.

With a quick glance, we can see that most classes have 29 students. We also know that in this survey, classrooms range in size from 26 students to 33 students. If this data was represented in a numerical, non-visual manner, it might have been more difficult for us to come to these conclusions.

## When Should We Use Line Plots?

Line plots are especially useful if your survey size is quite small. However, they might also be useful if you're dealing with the distribution of data over a small set. They're also an excellent choice if you want to draw attention to clusters or gaps in your data.

However, you can make your line plots as complicated as you like -- and it can help visualize surveys of the entire planet. As long as you group your data into smaller categories, a line plot can handle all kinds of data.

For example, you could run a survey on literacy rates throughout the world. Ten countries have a literacy rate of almost 100%, and you can group these together under one category in your line plot. However, there are many other countries that have literacy rates that are under 50%, and you can group these countries together in their own category as well. Some countries have literacy rates under 40%, while a single country (Chad) has a literacy rate below 30%. Each of these represents different categories in your line plot. We would put ten dots under the category of approximately 100% literacy while following the same pattern for other countries throughout the world. This shows how useful line plots can be for surveys that involve the entire population.

## What's the Difference Between a Line Plot and a Line Graph?

Line plots and line graphs are quite similar -- but it's important that we don't get these two concepts confused. A line graph connects data points with a continuous line, while a line plot does not. Line graphs are especially useful in helping us visualize changes over time. On the other hand, line plots are better suited to continuous data that doesn't change over time.

For example, a line graph might show us the improvement in literacy rates within a particular country over time. The x-axis (the horizontal line) might show us dates, such as the 1960s, 1970s, 1980s, and so on. The y-axis (the vertical line) might show us the literacy rates, such as $10%,20%,30%,$ and so on. Hopefully, we would see a country improving its literacy rate over time -- which means that the line would go up from left to right.

Both line plots and line graphs have x-axes and y-axes, but only line graphs have continuous lines.

## What's the Difference Between Line Plots and Bar Graphs?

Line plots and bar graphs are very similar. The only real difference is the way data is displayed visually. While line plots use dots to display frequency, bar graphs use (you guessed it) bars. Bar charts have the advantage that they can more easily represent fractional or other real valued numbers, whereas line plots are left only representing whole numbers. So if your data only involves whole numbers Line Plots are a great way to go.

## Types of Line Plots

There are two different types of line plots:

1. Wilkinson Line Plots

A Wilkinson line plot is the most familiar variety. Like the example we looked at earlier, this type uses numbers of dots to represent frequency. Sometimes, different colors are used for certain dots to represent special characteristics. For example, a red dot might represent a bilingual country, while a blue dot might represent a country with just one language.

1. Cleveland Line Plots

Cleveland line plots are a little different. Instead of writing out each dot, we can simply use the y-axis to show frequencies. For example, the y-axis might show a range of 1-30, allowing us to quickly see how many countries have a literacy rate of 100% or 50%. Many people think that Cleveland line plots are easier to read compared to Wilkinson line plots.

## A math tutor can help with applying data from line plots

If your student is struggling with applying data from line plots, private math tutoring can help. Working with a 1-on-1 instructor can help your student understand the math concepts that are involved in how to use line plots -- and more! Contact Varsity Tutors today, and we'll team your student up with a qualified educational professional whose experience matches up with your student's unique math goals.

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