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Learning Math Home
Data Session 7, Part A: Scatter Plots
 
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

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

Now that we have established that there is a positive association between arm span and height, a new question emerges: How strong is the positive association between arm span and height? Here again is the data for the 24 people:

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

In order to answer this question, let's note the mean arm span and height for these 24 adults:

 

Mean arm span = 175.5 cm

 

Mean height = 174.8 cm

Problem A4

Solution  

a. 

Is your arm span and height above the average of these 24 adults?

b. 

How many of the 24 people have above-average arm spans?

c. 

How many of the 24 people have above-average heights?

d. 

It is possible to divide the 24 people into four categories: above-average arm span and above-average height; above-average arm span and below-average height; below-average arm span and above-average height; and below-average arm span and below-average height. How many of the 24 people fall into each of these categories?


 

Problem A5

Solution  

a. 

Where would your arm span and height appear on the scatter plot?

b. 

Can you identify a person with an above-average arm span and height?

c. 

Can you identify a person with a below-average arm span and an above-average height?

d. 

Can you identify a person with a below-average arm span and height?

e. 

Can you identify a person with an above-average arm span and a below-average height?

Adding a vertical line to the scatter plot that intersects the arm span (X) axis at the mean, 175.5 cm, separates the points into two groups:


 

Problem A6

Solution  

a. 

Note that there are 12 arm spans above the mean and 12 below. Will this always happen? Why or why not?

b. 

What is true about anyone whose point in the scatter plot appears to the right of this line? What is true about anyone whose point appears to the left of this line?

Adding a horizontal line to the scatter plot that intersects the height (Y) at the mean, 174.8 cm, also separates the points into two groups:


 

Problem A7

Solution  

What is true about anyone whose scatter plot point appears above this line? How many such points are there?


 

Problem A8

  

Enter your own measurements or those of one of the other subjects you measured into the Interactive Activity below to plot these additional heights and arm spans against those of the people in the data set. Note that adding these measurements may affect the values of the means.


 
 

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity print this page, plot your additional measurements on the scatter plot in Problem A5, and calculate the new means.


Next > Part A (Continued): Quadrants

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