### Unit 7: Graphs and Charts

Once we have gathered data or performed calculations, we have to visualize the information to make sense of it. It is much easier to read a graph or chart than to interpret meaning from a long list of numbers. We use graphs and charts in almost every field. Businesses use graphs and charts to show trends in growth. Politicians use graphs and charts to explain demographics and voting trends in campaigns and elections. Since we use graphs and charts so often, it is important to know how to read and interpret them.

In this unit, we will discuss the different types of graphs and charts that we use in mathematics. We will interpret the results for each type of graph or chart, learn to create charts and graphs, read charts, and work with the measures of central tendency for a data set.

**Completing this unit should take you approximately 5 hours.**

Upon successful completion of this unit, you will be able to:

- determine the mean, median, mode, and range from a given set of data;
- represent and interpret data in a stem and leaf plot;
- represent and interpret data in a line graph;
- represent and interpret data in a bar graph;
- represent and interpret data in a box-and-whisker plot;
- represent and interpret data in a circle graph; and
- represent and interpret data in a pictograph.

### 7.1: Mean, Median, Mode, and Range

Before we begin constructing graphs and charts, we need to understand some basic statistics calculations that are often used to generate graphs and charts. Here, we will learn about four important statistical calculations:

**mean**,**median**,**mode**, and**range**.Read this section up to "Use the Basic Definition of Probability". Pay close attention to the summaries of how to do mean, median, and mode calculations. After you read, do examples 5.49–5.55 and check your answers.

Watch these three videos to see more examples, and to see what range means in the context of mathematics.

### 7.2: Stem-and-Leaf Plots

Now that we know the statistics needed to construct plots, we can begin exploring different types of graphs and charts. When you learn about each type of plot, should try to notice a few things. First, what type of data does the type of plot show? Second, what information is on each axis of the plot?

The first type of graph we will explore is the stem and leaf plot.Watch this video to learn about this type of plot.

After you watch the video, do the assignment and check your answers.

### 7.3: Line Graphs

The next type of graph we will explore are line graphs. Line graphs are often used to show trends over time or to show a distribution. For example, a line graph could be used to show the age distribution of students in a class. However, when looking at graphs, we must be careful to make sure that graphs do not misrepresent the data.

The first video explains the structure of a line graph using simple examples. The second video shows how line graphs can be manipulated to misrepresent data.

After you watch the videos, complete this assignment and check your answers.

### 7.4: Bar Graphs

Bar graphs are a common type of graph used to compare amounts or distributions.

Watch this video to see examples of bar graphs and their applications.

After you watch the video, do this assignment and check your answers.

If you would like extra practice, you can try this assignment.

If you want even more practice, you can try this assignment too.

### 7.5: Box-and-Whisker Plots

The shape of a box-and-whisker plot displays the spread of your data; it will show whether your data is normally distributed or skewed. When the median is in the middle of the box and the whiskers are about the same on both sides of the box, the distribution is symmetric.

These videos show examples of how box-and-whisker plots are used and examples of how to construct them.

After you watch the videos, take this assessment and check your answers.

### 7.6: Circle or Pie Graphs

The circle or pie graph is another graph that can be used to show distributions of data. For example, a pie graph can show the distribution of age ranges in the population of a city. The size of each slice of the pie corresponds to the percent of people in that age range.

Watch this video to learn how pie graphs are constructed and interpreted.

### 7.7: Pictographs

The last type of graph to discuss are pictographs. These use symbols to represent numbers of objects or people in a graph. In pictographs, it is important to read the key, or legend, to understand the meaning of the symbols.

Watch this video for an example of how to interpret a pictograph.

After you watch the video, do these exercises and check your answers.