Activity Title: Skeletons and Histograms Name: ______

The Research Experience for Teachers Program /
http://www.cs.appstate.edu/ret

Activity Title: Skeletons and Histograms Name: ______

Learning Objectives: Students will determine the shape, center, and spread of different distributions by analyzing histograms.

Materials List: computers, Kinect software, Microsoft Kinect device, spreadsheet software, Octave software

Introduction/Motivation:

Michael Phelps, an American Olympic swimmer, won 22 medals in his career making him the most decorated Olympian of all time. Contributing to his success are his unique height and wingspan. Phelps is 6 feet 4 inches tall, with a wingspan of 6 feet 7 inches. In this lab, you will be looking at the skeletal heights and wingspans yourself of your classmates in order to make comparisons and draw conclusions. The ability to make inferences based on data is an essential life skill.

Lab Activity:

Part 1

1. Open the “Skeleton Tracking” folder on the designated Kinect Desktop.

2. Open “Skeleton.exe” to run the Kinect Skeleton Recognition Software

3. Enter your name in the textbox. This is how your image will be saved.

4. Stand on the marker your instructor has placed on the ground and face the camera.

5. Stand with your legs together and hold your arms to the left and right to form 90o angles.

6. Hold still and say, “Freeze.”

7. Open up the “Skeleton Tracking” folder, find your image, and open it.

8. Open up the “Skeleton Tracking” folder, find your .csv file, and open it.

9. Look at both of these files side by side. Notice the (x,y,z) coordinates of your image.

10. Calculate your skeletal height by calculating the distance between your Head and your FootRight.

11. Calculate your skeletal wingspan by calculating the distance between your HandLeft and HandRight.

12. Open up the “Skeleton.xlsx” file on the Desktop.

13. Record your height and wingspan by typing the information into the appropriate columns of the “Skeleton.xlsx” spreadsheet.

Part 2

1. Open up Octave.

2. Create a row vector in Octave by typing:

> x = [1 3 2]

3. Create a column vector in Octave by typing:

> x = [1; 3; 2]

4. Create a 3 x 4 matrix in Octave by typing:

> A = [1 1 2 6; 3 5 8 7; 13 21 34 -2]

5. All variable you create stays in the memory, unless you clear them. To clear the vector x and A and any other variable in the buffer, you can type:

> clear all

6. Your instructor will provide the class data sets by either projecting the Skeleton.xlsx spreadsheet or sending you an email with the file.

7. Create a column vector (mhigh) that contains all of the heights of male students in our class.

8. Create a column vector (fhigh) that contains all of the heights of female students in our class.

9. Create a column vector (mwing) that contains all of the wingspans of male students in our class.

10. Create a column vector (fwing) that contains all of the wingspans of female students in our class.

11. Within Octave, there are many tools for statistical analysis. If you want to calculate the mean of a data set, you can use the command > mean (x) which will compute the man of the elements in vector x.

12. Complete the table below using Octave commands.

Mean / Median / Mode / Range / IQR / Standard Deviation
> mean (x) / > median (x) / > mode (x) / > range (x) / > Iqr (x) / > std (x)
Male Heights (mhigh)
Female Heights (fhigh)
Male Wingspans (mwing)
Female Wingspans (fwing)

Note: If there is no mode or the data set is bimodal, Octave will report the first number in the data set. Make sure to double-check your answer for mode.

13. Which measure of central tendency is most useful in describing the heights and wingspans of students in our class? Explain.

14. Which group (mhigh, fhigh, mwing, fwing) has the least variability? Which group has the most variability? Explain.

15. Oftentimes, it is helpful to see data more visually. In this case, you will examine histograms make comparisons and to draw conclusions.

9. Create overlapping histograms of your male and female height vectors by typing:

> hold on;

> hist(mhigh, 8, 1, “facecolor”, “g”);

> hist(fhigh, 8, 1, “facecolor”, “r”);

> hold off;

10. Describe the shape, center of spread of the male height distribution.

11. Describe the shape, center, and spread of the female height distribution.

12. Make two comparative statements about the male and female height distributions in our class.

15. Create overlapping histograms of your male and female wingspan vectors.

16. Describe the shape, center, and spread of the male wingspan distribution.

17. Describe the shape, center, and spread of the female wingspan distribution.

18. Make two comparative statements about the male and female wingspan distributions in our class.

Assessment

Results/Conclusions

Students should turn in a completed “Skeletons & Histograms Student Handout”

Reference(s)

http://en.wikipedia.org/wiki/Michael_Phelps

http://www.baltimoresun.com/sports/bal-phelpswingspan-flash,0,939651.flash

http://cs.appstate.edu/ret/sm13/activity.html