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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving9 chapters | 66 lessons

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*Betsy Chesnutt*

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Data is often presented in tables and graphs to make it easier to understand and interpret. In this lesson, you will learn about several types of tables and graphs, and develop the skills needed to understand them.

Fields as diverse as finance, science, and politics all rely heavily on interpreting large amounts of numerical data. This can be challenging for many people, and so tables and graphs are used to present the data in a way that is easy to understand.

Although there are many different types of tables and graphs, you can interpret them all if you remember some basic guidelines.

- First, look at the title and any other labels. Some graphs may have a legend that will give you important information. The axis labels can also tell you a lot about the information presented in the graph.
- Next, look carefully at the graph to identify the important information that you need to know and then use that information to answer the question.

Let's look at a few different types of tables and graphs and see how to understand the information presented in each.

Tables are the simplest way to represent data. A **table** compiles all the data into a columns and rows so that it can be easily interpreted. The table below shows the average number of visitors per day at two different lakes over an eight year period. By looking at the row and column titles, you can see that each row corresponds to a different year, and each column to a different lake.

You could use a table like this to answer a lot of different questions. For example, which lake had more visitors in Year 5?

The table shows that in Year 5, Lake Itawamba had an average of 74 visitors per day and Lake Tishomingo had an average of 85 visitors per day, so Lake Tishomingo had more visitors in Year 5.

A **pictograph** uses images to to represent a certain number of items. For example, suppose you had a lemonade stand and wanted to record how much lemonade you sold each day. Using the following pictograph, determine how many glasses of lemonade you sold on Thursday:

Did you get 40 glasses of lemonade? Great!

Looking at the pictograph, you can see that there are four lemons on the line that says Thursday, and you also know that each lemon represents 10 glasses of lemonade. This means that you sold 40 glasses of lemonade on Thursday.

A **line graph** plots individual data points as dots and connects them with lines. These are great if you want to see how a quantity is changing over time. The line graph below represents the distance an object travels over time. Even though there is no title, you can look at the axis labels and see that the x axis measures time and the y axis measures distance.

Using this graph, you could find the position of the object at any time. You could also use this graph to determine that the object was speeding up, because the difference in distance between any two consecutive seconds is increasing.

**Bar graphs** use bars of different heights to represent data. As with the other types of graphs, you first want to read the title and the axis labels to make sure you understand what data is being presented. In the bar graph shown below, you can see that the x axis has months and the y axis says Temperature. Therefore, this graph is showing you the average temperature during each month of the year at a certain location.

Now you are ready to analyze and use the data presented in the graph. Can you use the graph to calculate the temperature difference between the warmest and the coldest month of the year?

First, you need to determine which month is the warmest and which is the coldest. Looking at the graph, we can see that January is the coldest and July is the warmest. Next, note the average temperatures in both January and July. In this graph, the average temperature in January is about 30 degrees and the average temperature in July is about 75 degrees. Finally, subtract the two temperatures to find the temperature difference:

75 degrees - 30 degrees = 45 degrees

A **circle graph**, also known as a pie chart or pie graph, divides a circle into sections to represent the relative sizes of each category. Circle graphs are great for showing relative sizes, although they don't typically show the absolute numbers of any category. For example, a circle graph of the ages of people in a city might show that 43% of the citizens are under the age of 30, but it wouldn't say exactly how many people are under age 30.

Look at the circle graph below and see if you can determine what data is being presented.

This is a graph of the dinner selections made by clients of a catering company, and it has a legend that tells you what each color represents. The owner of the company might use a graph like this to determine how many of each type of dinner to produce for an event.

What if the company was hired to cater a dinner for 400 people? About how many chicken dinners should they prepare?

You can answer this question using the circle graph. From the graph, you know that 46% of people typically choose the chicken dinner, so if there are 400 people total attending the dinner, you can calculate how many chicken dinners to prepare.

46% = 46/100

x = 400 x (46/100) = 184 chicken dinners

No matter which type of graph you are looking at, you want to always first read all the labels and try to understand exactly what the graph is showing you. Then, analyze and use the data to answer the question.

**Tables**compile data into a list or group of lists.**Pictographs**use images to represent a certain number of items.**Line graphs**plot individual data points as dots that are connected by lines and are used to show trends over time.**Bar graphs**use bars of different heights to represent data.**Circle graphs**, or pie charts or pie graphs, divide a circle into sections to represent the relative sizes of each category.

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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving9 chapters | 66 lessons

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