Lesson 22

What do you Notice? What do you Wonder?

Your teacher will give you a set of cards. Each card shows a scatter plot.

1. Sort the cards into categories and describe each category.
2. Explain the reasoning behind your categories to your partner. Listen to your partner’s reasoning for their categories.
3. Sort the cards into two categories: positive associations and negative associations. Compare your sorting with your partner’s and discuss any disagreements.
4. Sort the cards into two categories: linear associations and non-linear associations. Compare your sorting with your partner’s and discuss any disagreements.

Is there an association between the weight of an animal’s body and the weight of the animal’s brain?

animal	body weight (kg)	brain weight (g)
cow	465	423
grey wolf	36	120
goat	28	115
donkey	187	419
horse	521	655
potar monkey	10	115
cat	3	26
giraffe	529	680
gorilla	207	406
human	62	1320
rhesus monkey	7	179
kangaroo	35	56
sheep	56	175
jaguar	100	157
chimpanzee	52	440
pig	192	180

Use the data to make a scatter plot.  Are there any outliers?

Experiment with the line to fit the data. Drag the points to move the line. You can close the expressions list by clicking on the double arrow.

 

1. Without including any outliers, does there appear to be an association between body weight and brain weight? Describe the association in a sentence.
2. Adjust the line by moving the green points, fitting the line to your scatter plot, and estimate its slope. What does this slope mean in the context of brain and body weight?
3. Does the fitted line help you identify any other outliers?

Sometimes a scatter plot shows an association that is not linear:

We call such an association a non-linear association. In later grades, you will study equations that can be models for non-linear associations.

Sometimes in a scatter plot we can see separate groups of points.

We call these groups clusters.

People often collect data in two variables to investigate possible associations between two numerical variables and use the connections that they find to predict more values of the variables. Data analysis usually follows these steps:

1. Collect data.
2. Organize and represent the data, and look for an association.
3. Identify any outliers and try to explain why these data points are exceptions to the trend that describes the association.
4. Find n equation that fits the data well.

Although computational systems can help with data analysis by graphing the data, finding an equation that might fit the data, and using that equation to make predictions, it is important to understand the process and think about what is happening. A computational system may find an equation that does not make sense or use a line when the situation suggests that a different model would be more appropriate.