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Learning Math Home
Data Session 7: Bivariate Data and Analysis
 
Session 7 Part A Part B Part C Part D Homework
 
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Session 7 Materials:
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Session 7, Part A:
Scatter Plots (45 minutes)

In This Part: A Bivariate Data Question | Building a Scatter Plot | A Further Question
Quadrants

Have you ever wondered whether tall people have longer arms than short people? We'll explore this question by collecting data on two variables -- height and arm span (measured from left fingertip to right fingertip).

Ask a Question
One way to ask this question is, "Is there a positive association between height and arm span?"

Through this question, we are seeking to establish an association between height and arm span. A positive association between two variables exists when an increase in one variable generally produces an increase in the other. For example, the association between a student's grades and the number of hours per week that student spends studying is generally a positive association. A negative association, in contrast, exists when an increase in one variable generally produces a decrease in the other. For example, the association between the number of doctors in a country and the percentage of the population that dies before adulthood is generally a negative one.

There are many other ways to ask this same question about height and arm span. Here are two, which we will concentrate on in Part A:

 

Do people with above-average arm spans tend to have above-average heights?

 

Do people with below-average arm spans tend to have below-average heights?

Collect Appropriate data
In Session 1, measurements (in centimeters) were given for the heights and arm spans of 24 people. Here are the collected data, sorted by increasing order of arm span:

Person #

Arm Span

Height

1

156

162

2

157

160

3

159

162

4

160

155

5

161

160

6

161

162

7

162

170

8

165

166

9

170

170

10

170

167

11

173

185

12

173

176

 

Person #

Arm Span

Height

13

177

173

14

177

176

15

178

178

16

184

180

17

188

188

18

188

187

19

188

182

20

188

181

21

188

192

22

194

193

23

196

184

24

200

186

This is bivariate data, since two measurements are given for each person.

Problem A1

Solution  

The data given above are sorted by arm span. Are they also sorted by height? If not exactly, are they generally sorted by height, and, if so, in which direction? Does this suggest any type of association between height and arm span?


 

Problem A2

Solution  

a. 

Measure the arm span (fingertip to fingertip) and height (without shoes) to the nearest centimeter for six people, including yourself.

b. 

Does the information you collected generally support or reject the observation you made in Problem A1?

c. 

Identify the person in the table whose arm span and height are closest to your own arm span and height.


Next > Part A (Continued): Building a Scatter Plot

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