Lesson Plan - Get It!
When you look at a bunch of numbers and want to say something meaningful 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
Right now, this is just a list of numbers that doesn't make any sense. I haven't even told you what they represent yet.
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 right answers here, and there are no wrong answers either. Jot down in your notebook what you observe.
Now that you have made some observations, let me tell you 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 to that question.
You may have noticed the highest and lowest numbers. You may have noticed that there are a few numbers that come up many times and a few numbers that only come up once or twice.
However, it is still difficult to say much about the calories in breakfast cereals when the data is arranged in this list.
Statisticians have the same problem when they look at lists of numbers. They make observations and they ask questions, just like you just did.
However, the next step for a statistician is to organize the data in a way that makes it more meaningful.
Let's explore how they do that.
You may have heard it said that a picture paints a thousand words. A picture can also represent a thousand data points.
In our case, let's look at a picture of our 76 data points:
- That at least looks 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 your own ideas, write down a brief description of the shape of our data on cereal calorie counts.
It probably won't surprise you that statisticians use specific words to describe the shape of data sets. That doesn't make your description wrong if you didn't use those same words.
The main reason for using specific words is so 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 skew left in your own words.
Now, compare your definitions to these formal definitions:
A symmetric 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 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 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 of the data 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.
We started with a list of 76 numbers that made little sense in just a list.
By drawing a picture of the data we could see more. The picture gave us an idea of the shape of the data. We could see the largest and smallest values more easily, which helped us find the range of the data. Lastly, we considered the idea of the center of the data set.
These are some of the basic building blocks for understanding data sets and starting to interpret them.
In the Got It? section, you will have the opportunity to consider these ideas and terms further.