Numb3ers: How Tall Is the Criminal?

Numb3ers: How Tall is the Criminal?

Project Details: Agent Eppes is tracking an unknown criminal. As the criminal was escaping the crime scene, witnesses saw him jump out of a window and land on his side in wet grass. Much of the impression of the criminal is obscured by footprints, but the criminal’s leg from knee to hip was measured to be 47 cm.

Agent Eppes has taken this information and thinks that there is a relationship between the height of a person compared to the length of his or her femur (the bone in your leg from your hip to your knee). If there is a direct relationship, Agent Eppes would like to use this information to describe the criminal in as much detail as possible. Others in the FBI have told him there is some sort of relationship between a person’s height and his/her arm span (the width of your arms when held out parallel to the floor). Another agent has said there should be a direct relationship between height and the length of a person’s foot. You are here to assist Charlie with finding these relationships and this is your assignment.

Step 1: With a partner complete the following table with measurements from your body and measurements from all your classmates. Measure the length along the outside of your leg from hip to knee as you sit in a chair. Measure your height using a ruler to mark your height along a flat wall and measuring straight down. Use a marker and the paper provided to measure your arm span along a flat wall. Take off your shoes, and mark your foot length on the paper provided then measure the paper on a flat surface. Make all your measurements in centimeters.

Height (cm) Femur Length (cm) Arm Span (cm) Foot Length (cm) Height (cm) Femur Length (cm) Arm Span (cm) Foot Length (cm)

Step 2: Plot your data by hand on the following grids provided in order to compare your height to each of the other measurements to check for relationships (correlations). Step 3: Describe the pattern you see in graph 1 – Height vs. Femur length. Does there seem to be a relationship (correlation) between your height and the length of your femur bone? If there is a relationship, explain the relationship. (Positive Correlation, Negative Correlation, No Correlation, Strong or Weak Correlation)

Step 4: Describe the pattern you see in graph 2 – Height vs. Arm Span. Does there seem to be a relationship (correlation) between your height and the length of your arm span? If there is a relationship, explain the relationship. (Positive Correlation, Negative Correlation, No Correlation, Strong or Weak Correlation)

Step 5: Describe the pattern you see in graph 3 – Height vs. Foot length. Does there seem to be a relationship (correlation) between your height and the length of foot? If there is a relationship, explain the relationship. (Positive Correlation, Negative Correlation, No Correlation, Strong or Weak Correlation) Step 6: Agent Epps need to be able to use these relationships to help solve this case and other cases in the future; therefore, he needs an algebraic rule (function rule) for finding height from a femur length, finding height from an arm span, and finding height from foot length. Take your graphing calculator and using your table of data, perform the correct regression to model the relationship shown in each of your three graphs. (In other words, find the equation for the line of best fit in each graph)

Height vs. Femur length equation: ______

Look at your correlation coefficient: How reliable is this equation for making predictions? Explain your thinking.

Height vs. Arm span length equation:______

Height vs. Foot length equation:______

Step 7: Using your relationships.

1. Use your equation from graph 1 – Femur vs. Height - find the height of the escaping criminal who's femur was 47 cm long. 2. Anthropologists have developed a formula to determine the height from femur length. In cm, a man's height is given as y = 2.59(femur length) + 66.4. Use this rule to find the height of the escaping criminal. How do the two heights compare?

3. What might explain the diffrences in the height that you found using the scatterplot and the anthropologists' formula y = 2.59x + 66.4 where x is the femur length.

4. Agent Epps needs more information to track the criminal. Using your height from the official formula (y = 2.59x + 66.4) find the arm span and foot length of the criminal by using your other linear regression models (equations).

1. Arm span______

2. Foot Length______

5. Calculate the approximate height of a criminal who has a foot length of 12 cm.

6. Calculate the approxiate arm span of a criminal who has a height of 140 cm. 7. Calculate the height of a criminal who has a femur length of 36 cm (using your regression model)

8. Calculate the foot length of a crimial who is 163 cm tall.

9. Calculate the height of a criminal who has an arm span of 100 cm.

10. Calcualte the approximate height of a criminal who has a foot length of 10 cm.

11. Calculate the femur length of a criminal who is 120 cm. Tall (using your regression model)