Picture This! Using Visual Representations of Data

Lesson Plan - Get It!

Audio:

When you examine a large group of numbers and want to make meaningful statements about them, you need ways to organize them.

Take these numbers.

70, 120, 70, 50, 110, 110, 130, 90, 90, 120, 110, 120, 110, 110, 110, 100, 110, 110, 110, 100, 110, 100, 100, 110, 110, 100, 120, 120, 110, 100, 110, 100, 110, 120, 120, 110, 110, 110, 140, 110, 100, 110, 100, 150, 150, 160, 100, 120, 140, 90, 130, 120, 100, 50, 50, 100, 100, 120, 100, 90, 110, 110, 80, 90, 90, 110, 110, 90, 110, 140, 100, 110, 110, 100, 100, 110

This is just a list of numbers that makes no sense. What they represent is not yet indicated.

Take 5 to 7 minutes to look at the data and allow yourself to make some observations.

• What do you see?
• What do you wonder?
• How might you organize it so that it makes more sense?

There are no correct answers here, and there are no wrong answers either. Jot down what you observe in your notebook.

Now that you have made some observations, learn what the data represents. These are the calorie counts for one serving of 76 different kinds of breakfast cereal.

• Does knowing that change your thinking at all?

Again, there is no right or wrong answer, but take the time to write down your answer.

You may have noticed the highest and lowest numbers. You may have noticed that a few numbers come up many times, and a few only come up once or twice.

However, when the data is arranged in this list, it is still difficult to say much about the calories in breakfast cereals.

Statisticians have the same problem when looking at lists of numbers. They make observations and ask questions, just like you did.

However, the next step for a statistician is to organize the data in a way that makes it more meaningful.

Explore how they do that.

You may have heard a picture paints a thousand words. An image can also represent a thousand data points.

In this case, look at a picture of the 76 data points.

• That seems a little better now, doesn't it?

Trying using this picture to answer these questions.

Look at that picture, called a histogram, of the data again.

Using your own words and ideas, briefly describe the shape of the data on cereal calorie counts.

It probably won't surprise you that statisticians use specific words to describe the shape of data sets. However, your description would not have been wrong if you hadn't used those exact words.

The main reason for using specific words is that everyone understands the general shape from just a few words. The words that statisticians use are symmetric, skew left, and skew right.

Here is a picture of a symmetric set of data.

Write down a definition of symmetric in your own words.

Here is a picture of data that is skew right.

Try writing a definition of skew right in your own words.

Lastly, here is a picture of data that is skew left.

Try writing a description of the skew left in your own words.

Now, compare your definitions to these formal definitions.

The asymmetric data set is roughly the same shape on both sides of the center. There is about the same amount of data on the right of the center as there is on the left of the center.

A skew right data set trails out to the right with a small amount of data on the right of the center. The majority of the data is left of the center.

A skew left data set trails out to the left with a small amount of data on the left of the center. The majority of the data is right of center.

The center of a data set can be thought of in different ways.

One way to think of the center is the average, which statisticians call the mean.

Another way to think about the center is the point where half of the data is less and half is more. Statisticians call this the median.

A third way, which is much less common for a statistician to talk about, is the most common data point, called the mode.

You started with a list of 76 numbers that made little sense in just a list.

Drawing a picture of the data helped you see more. The picture gave you an idea of the data's shape.

You could see the largest and smallest values more efficiently, which helped you find the data's range. Lastly, you considered the idea of the data set's center.

These are some of the basic building blocks for understanding data sets and starting to interpret them.

In the Got It? section, you can consider these ideas and terms further.