Statistical Analysis of Graphs

Experiment 1

In order to determine how the concentration of pollen in the air changed with elevation, a researcher fitted a weather balloon with an altimeter and devise for measuring the concentration of pollen. The device was programmed to sample the air temperature every 500 meters and radio the results to a receiver on the ground. The following data was obtained:

Altitude (km) Pollen (particles/ml)

0.5 288

1.0 137

1.5 99

2.0 75

2.5 58

3.0 44

3.5 42

4.0 38

4.5 32

Experiment 2

A SCUBA diver wanted to know water pressure changes with depth, so she swam down to several predetermined depths in the water, then checked the pressure. She calibrated the pressure gage to read “zero” at the surface (no water pressure).

Depth (feet) Water Pressure (atmospheres)

0 0

24 0.8

41 1.3

60 1.8

75 0.2

81 2.6

100 3.2

117 3.6

Statistical Analysis of Graphs

Enter the data for each experiment in Logger Pro.

Manually set your axes to fit the range of your data.

Choose the best option from the “Analyze” drop down menu.

Experiment 1

1. What was the manipulated variable? Manipulated variable is always the x-axis

2. What type of relationship exists between the variables?

3. Give the specific equation for the data set: substitute “Pollen” for Y and “Altitude” for X

4. Use the equation to predict the concentration of pollen at an altitude of 8.6 kilometers:

pollen = 143 / 8.6 km

5. Use the equation to predict the altitude if the pollen concentration is 12 particles/ml:

12 = 143 / altitude

Experiment 2 (clear all data from Experiment 1 before continuing)

1. What was the responding variable in this experiment?

2. Plot the data and look at the graph. Which data point is an obvious outlier?

3. What type of relationship exists between the variables? proportional

4. What is the RMSE for the equation if you keep the outlier in the data set?

Explain what is wrong with the best fit line:

(in what way does it not fit well)

5. Remove the outlier from the data table by highlighting the bad value, hitting the backspace button, then

arrow down off the removed data point.

What is the new RMSE for the equation if you take the outlier out of the data set?

6. What does a low RMSE value tell you about your data? The line is a better fit

7. Give the specific equation for the data set:

8. Use the equation to predict the pressure at the bottom of the Marianas Trench (depth = 35,798 feet):

9. Use the equation to depth of water that is equivalent to one atmosphere of water:

1 atm = .03136 * depth solve for depth