Copland College

Applying Statistics - 2006
Investigative Task

Can the length of a bone in your arm be used as a predictor of a person's height?

The investigation that you will carry out here has its origin as part of Police Forensic work on the identifications of bodies.  Generally a body can be identified by the use of dental records or from fingerprints.  However, if only a few bones of a victim are found then it makes identification much more difficult.  However, forensic anthropologists, i.e., scientists who study the bones of people in an effort to paint a portrait of their former life,  are able to determine a person's height from the measurements of the length of various bones in the arm or the legs.  Generally bones from the legs give a better estimate of a person's height than do bones from the arms. The formulas that we will use in this activity apply particularly to adults who have fully developed skeletons.  Part of our investigation will be to examine how well the data that we collect agrees with the formulas as well as a comparison with data from a group of year 9 students. 

In this exercise you will do the following,

a) Have your height measured to the nearest centimetre.

b) Measure the length of the RADIUS bone in your arm.

c) Collate data for all the students in your class.

d) Analyse the data using Excel.

e) Assessment: Hand in your original data sheet, a computer print out of your data sheet and graphs.  You will be assessed on the quality of your work and the amount of work that you are able to complete. You may work with a partner or group to collect the data, however, the analysis must be done individually.  You must show the graph to your teacher before it is printed.  All computer generated sheets must have your name computer printed on them.

A picture of the human skeleton is shown below.  The names of the various bones are also given.  Note the position of the Radius (#11) and the Tibia (#22).  If you would like to look at other bones of the human body click the following link http://www.bio.psu.edu/faculty/strauss/anatomy/skel/skeletal.htm  

You will have been given a data sheet which you are to record your data and the data from everybody else in the class.

Measuring your height: Work with a partner or with a group.  If you have high shoes then they should be removed.  Stand against a wall in the classroom.  Your partner will then take a book.  One edge of the book is placed against the wall and the other on the top of your head.  Hold the book in position as the person moves away.  Mark the height carefully on the wall and then with the measuring device supplied measure the height of the person.  Record this on the sheet.

Radius Length:  It is difficult to measure the length of the radius in your arm.  However a reasonable estimate can be obtained by measuring from the outside of your wrist to the tip of your elbow.  Record the value on the table.  Make this measurement as accurate as possible.

Analysing the Data:

The following data was obtained from another group of students.  Your data sheets will contain similar data.  The data from Tables 1 and 2 can be copied directly to an Excel spreadsheet. 

Table 1 Table 2
Male Data - Radius Length(cm) Female Data- Radius Length(cm)
Person Radius Height Person Radius Height
A 27 165 K 26 162
B 26 172 L 23 151
C 28 173 M 24 169
D 27 166 N 24 165
E 29 173 O 26 155
F 38 188 P 24 156
G 30 177 Q 25 163
H 28 170 R 27 167
I 26 167 S 26 171
J 28 181 T 28 168

The formulas that relate to radius length and to tibia length are shown in the table below.  In this exercise we will only complete the activity for radius length.

Table 3 Table 4
Male Height (cm) Female Height (cm)
3.3 x (radius) + 84.6 3.3 x (radius) + 80.0
2.4 x (tibia) + 77.4 2.4 x (tibia) + 73.6

These formulas can be read in the following fashion.  

Male Height = 3.3 x (radius length) + 84.6   - the answer will be expressed in centimetres

We will use the spreadsheet to do all of the calculations and graphing.

Open Excel and type the headings as shown below.  Row 1 is 12 point text, bold the remainder is 10 point bold

Note that the Calculated Height column has text that is "wrapped".  To "wrap" text right click on the cell D2.  You should see the following dialog box.

From the Format Cells menu check the Wrap text "check box".

 

Using the formulas:

Enter the formula for predicting the males height into cell D3.  See diagram below.

This formula is then copied and pasted down column D for each person that is listed.

Look carefully at the following screen image to determine how the formula should be written.

Note the = (equals sign) at the start of the formula.  This tells Excel that what follows is to be read as a formula rather than a number or text.

Your task now is to repeat the process for the females in column H.  Remember the formula for females is slightly different.  Click here to review the formulas again.  

Graphing: 

We will use Male's Data - Radius Length to show you how to complete the graphing.   To graph the data and therefore to compare the predicted vs the actual height highlight the data in columns A, B, C and D the data will first be sorted.  The male's data needs to be sorted separately to the female's data.

The data will be sorted numerically based on radius length. It will be sorted from lowest to highest - ascending.  Select cells as shown below.  Don't include Row 1.

  

From the Data  menu choose Sort.  You should see the following,

Make sure that Header row is checked and that it is being sorted by Radius.  Once you click OK your data should look similar to than shown below.

Click the graphing icon on the menu bar , choose Line Graph.  When the chart wizard appears choose the following options.

Your aim is to produce graphs for both males and females that looks similar the one shown in the diagram below.  Each graph is required to be printed and handed in for marking.  Work through the Chart Wizard - Chart Options dialog box to set titles, legend and other graph variables,

Question 1:  When you have completed the graphs for males and female height based on radius length answer the following.  By looking at the graphs produced how good  have the equations been in predicting the height of the males and females.   Have the predicted heights appeared more accurate for the males or the females or does each equation do a reasonable job at predicting?  

Lines of Best Fit - How well do these equations predict your height.

Our next task is to produce a scatter - plot of radius length vs actual height and predicted height.  We will be checking the relationship between the length of the radius and your height.  For this we will have Excel draw a line of best fit and we will then have Excel examine the correlation between these two quantities.

Select data from your data sheet as shown below.  

Click the graphing icon,   Choose the scatter-plot option as shown below.

Some of the options such as graph titles and axes titles can be seen in the graphic below.

The graph that is produced looks similar to the following. Note that if you right click on the graph you can choose the location where it will be displayed.  The options are beneath the graphic below.  

When your print your graph first change its location from the Chart location dialog box.  Right click on any chart and select Location from the menu.  Choose As new sheet for a large graph or As object in for a small graph.  Always print a graph after selecting As new sheet.

To change the scale on the x-axis right click on the horizontal axis.

When the Format Axis dialog box appears choose the options as shown below.

Repeat the procedure for the vertical axis.  Choose a minimum value of about 150.

You final graph should look similar to the following.

Creating a line of best fit:  

To draw a line of best fit right click on the blue line (actual height).

Choose the Add Trendline option.  Keep the default value of Linear  and then click the Options tab

Your graph should now have a line of best fit as well as the equation for the line.  The R-squared value is an indicator that ranges in value from 0 to 1 and reveals how closely the estimated values for the trendline correspond to your actual data. A trendline is most reliable when its R-squared value is at or near 1.  When it is 1 there is a good correlation between the two sets of data being graphed.  The higher the R-squared value then the better is the length of the radius as a predictor of a person's height.

The R-squared value in the graph above shows that the radius length was a reasonable predictor of a persons height.  Your data might show otherwise.

Repeat this graphing procedure for the females of the class.  You will need to print all graphs when they are completed.  Make sure that your name is printed on each graph.

When you have completed the line of best fit analysis for both males and females answer the following question.  

Question 2: Look carefully at the graphs for boy's and girl's height based on the length of the radius.  Comment on how the calculated heights and the actual heights compared.  Do they generally agree, are there any significant differences?  Do the formulas predict boys height better than girls height or vice versa? 

Question 3: The tallest identical female twins in the world were Heidi and Heather Burge.  The play basketball in the USA.  They have a height of 6 feet 4 3/4 inches.  Convert this to centimetres using the following information.  12 inches = 1 foot and 1 inch is 2.54 cm. To help you with this conversion you can visit the online calculator at http://www.worldwidemetric.com/metcal.htm  To use this you will need to convert the 6 feet 4 3/4 inches to decimal form.  To do this you need to find what fraction of 1 foot is 4 3/4 inches.  This is done by dividing 4 3/4 by the number of inches in 1 foot.  This is of course 12 inches.  You can use your spreadsheet for this.

Using your spreadsheet  try to calculate the radius length of these girls based on the formulas that you have been using.  This will be done by a trial and error process

Set up your spreadsheet as follows ,

What you will need to do now is to type values into cell A2  so that the the height displayed in cells B2 is equal to the height that you have just determined for the basketball girls.

Question 4:  How does these length of the Radius of these girls compare to your length of your radius and tibia?  :Calculate the length of you radius as a percentage of Heidi and Heather Burge's radius length.