Activity – Scatter Plot Relationships and the Golden Ratio Academic Probability and Statistics
Name ________________
Directions: 1. You and a partner are to measure each other’s height, arm span (the length from fingertip to fingertip when your arms are spread out), and the height of each person’s belly button (BBH) to the floor (all in inches). Record your information: Height: _______ Arm span: _______
Height of belly button (BBH) to the floor: _______
Record your information on the class overhead and copy the entire class data on the back of this sheet. 2. Who are the individuals in this study? 3. What exactly are the variables? How are they measured? Are they categorical or quantitative? 4. Make a scatter plot of height vs. arm span. 5. Make a scatter plot of height vs. BBH. 6. Find the correlation for height vs. arm span and height vs. BBH. 7. Calculate and draw the least squares regression lines on each graph. 8. Estimate the arm span and BBH for a person who is 67” tall. 9. Describe the overall pattern of each graph. Describe what the association means in terms of the problem situations. a. Is height a good predictor of arm span? b. Is height a good predictor of BBH? 10. In the table, fill in the Height/Arm Span and Height/BBH columns by dividing each person’s height by the given variable. a. Find the mean of the data in both columns. b. What do these means tell you in terms of the problem situation? Extra Credit: The mean that you found in the Height/BBH column should be close to a special number called the Golden Ratio. Write at least 2 well constructed paragraphs about the golden ratio. What is the golden ratio? What is the history of the golden ratio? How old is it(predicted)? How is it seen in objects around the world and what are some of the objects? Who are some famous people who used the golden ratio? Why is the golden ratio so important?
Student Name
Height (in.)
Arm Span(in.)
BBH (in.)
Height/AS
Height/BBH
Mean: _____ Mean: ______