Session 7, Part A:
Scatter Plots

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

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

 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

 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

 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 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.