Session 7, Part A:
Scatter Plots

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

We will now begin our analysis of the bivariate data and explore the co-variation in the arm span and height data. Here again are the collected arm spans and heights for 24 people, sorted in increasing order by 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

Bivariate data analysis employs a special "X-Y" coordinate plot of the data that allows you to visualize the simultaneous changes taking place in two variables. This type of plot is called a scatter plot. Note 1

For our data, we will assign the X and Y variables as follows:

X = Arm Span
Y = Height

To see how this works, let's examine the 10th person in the data table. Here are the measurements for Person 10:

X = Arm Span = 170 and Y = Height = 167

Person 10 is represented by the coordinate pair (170, 167) and is represented in the scatter plot as this point:

Let's add two more points to the scatter plot, corresponding to Persons 2 and 23:

Person #

Arm Span

Height

 2 157 160 23 196 184

Here is the completed scatter plot for all 24 people:

Problem A3

Judging from the scatter plot, does there appear to be a positive association between arm span and height? That is, does an increase in arm span generally lead to an increase in height?

 Video Segment In this video segment, Professor Kader introduces bivariate analysis. The participants measure their heights and arm spans and then create a scatter plot of the data. Professor Kader then asks them to analyze the association between the two variables, height and arm span. If you're using a VCR, you can find this segment on the session video approximately 4 minutes and 34 seconds after the Annenberg Media logo.

 The scatter plots illustrate the general nature of the association between arm span and height. Reading from left to right on the horizontal scale, you can observe that narrow arm spans tend to be associated with people who are shorter, and wider arm spans tend to be associated with people who are taller -- that is, there appears to be an overall positive association between arm span and height.

 Session 7: Index | Notes | Solutions | Video