HSC Mathematics General 2 – How big is that Yowie?
Outcomes Assessed
MG2H-1 uses mathematics and statistics to evaluate and construct arguments in arange of familiar and unfamiliar contexts
MG2H-2 analyses representations ofdata in order to make inferences, predictions andconclusions
MG2H-3 makes predictions about situations based on mathematical models, including those involving cubic, hyperbolic or exponential functions
MG2H-5 interprets the results ofmeasurements and calculations and makes judgements about reasonableness, including the degree of accuracy ofmeasurements and calculations and the conversion to appropriate units
MG2H-7 answers questions requiring statistical processes, including the use of the normal distribution, and the correlation of bivariate data
MG2H-9 chooses and uses appropriate technology tolocate and organise information from a range ofcontexts
“We of the Blue Mountains local area are extremely concerned. Since the recent bushfires here, there have been more sightings of a yowie.”
“Please help us to determine the height and weight of the creature discussed in the ABC program and the news articles below “http://bit.ly/1Fvw4Uj
Task
The following task is split into Part A, B and C. You are also required to keep a journal of your progress and show this to you teacher in each lesson.
Part A - Scatter plot, modelling the relationship and predicting (11 marks)
1. Take a random sample of 20 down load as an excel file, save and name it as HSCTASK.2. Select the questions that reveal the Belly button height (h) and arm span(S).
3. Copy the required data [Belly button height (h) and arm span(S) ] from your downloaded data, paste it in a new sheet named Part A, ensure that the Belly button height is the independent variable, Save.
4. Copy and paste this same data, leaving a one column space between the data sets.
5. Delete the invalid pairs in the new set
6. Print off the two data sets, labelled, ‘Raw data part A’, & ‘Checked data part A’ and indicate which pairs you eliminated in the first set and your reasons for doing so. Save. / 2 Marks
7. In your Part A sheet create a scatter plot using insert scatter plot.
8. Add appropriate extra grid lines and print your graph A4 size labelled ‘Checked data part A’
9. With your printed graph ‘by eye’ draw a line of fit to represent the trend shown.
10. Determine to 1 decimal place the gradient and the y intercept of your line of best fit. State your equation (model of the relationship) between the two variables. / 4 Marks
11. Comment on any limitations your model / 1 Mark
12. A small yowie was sighted and has left an arm span (S) print of 100 cm in sandy soil. Using your equation predict the its belly button height (h) / 1 Mark
13. Another yowie was sighted with a belly button height of 1.5m. Using your equation predict its arm span (S) to 1 decimal place / 1 Mark
14. Previous scientific studies on humans show there is a strong correlation between of height of a person (H) and their belly button height (h), H = 2.3h Assuming Yowies fit the model, use this and your previous determination of belly button height (h) to predict the height of the small Yowie to 1 decimal place / 1 Mark
15. Studies also indicate that weight could also be predicted from Wt (kg) = 0.79 x (Height in cm) – 44.9
Use this to predict the weight of the yowie to nearest kg. / 1 Mark
Part B (3 marks)
1. Download a different sample of 200 from the Census at school random sampler.2. Choose the right foot length (independent variable) and dominant hand reaction time from the data set you downloaded copy and paste this as Part B in another sheet in your original excel file HSCTASK.
3. Copy and paste this same data, leaving a one column space between the data sets.
4. Create an appropriate scatter plot; Label it ‘Raw Data part B’. Print it and inspect the points.
5. Mark any inappropriate/invalid data pairs on your ‘Raw Data part B’ graph, delete any inappropriate/invalid data pairs in the new set and save. / 2 Marks
6. Now print your new graph, labelled ‘Graph Part B’, comment on the correlation, (suggest what type and approximate the correlation coefficient). / 1 Mark
Part C - Using excel to determine the line of best fit y = mx + b using least squares method. (22 marks)
From the same sample set in Part B, select the columns containing the (independent variable) right foot size (f) and height (h). Repeat steps 2 & 3 of Part B pasting in another sheet named Part C. Check the data pairs & eliminate any you feel are inappropriate / invalid, save the checked data pairs similar to steps 4 & 5 in Part B.
1. Create an appropriate scatter plot with suitable gridlines, maximum & minimum scale values. / 1 Mark2. On your excel spreadsheet sheet Part C determine the appropriate values (to 2 decimal places) to form the least squares line of fit. Print your graph labelled Part C Graph and draw the least squares line of fit by hand. / 10 Marks
3. Use this least squares method line to graphically predict the height of the yowie given that the foot print found was 43 cm. / 1 Mark
4. By how much would the yowies height increase if the foot length now increases by 1 cm? Explain your answer. / 2 Marks
5. Determine the percentage error for the 43 cm foot, comment on your value compared to your correlation coefficient. Assume the precision of the measuring device used was 1 cm? / 3 Marks
6. Given that Yowies are similar to humans and are born with an average foot size of 5 cm what would be the expected height of a new born Yowie? What limitations may exist for the least squares line of best fit model of yowie foot & height? / 1 Marks
7. What limitations may exist for the least squares line of best fit model of yowie foot and height? / 3 Marks
8. Given all the information you have collected and graphed, and the attached sheet age percentiles (Boys & Girls) at what age would you estimate the small yowie in task 1 part 14 to be? / 1 Mark
What to submit and where?
· In Moodle, submit your excel spreadsheet ‘HSCTASK’ that includes the sheets Part A, Part B and Part C with the calculated values and excel formed graphs included on the sheets.’
· Hand in to your teacher, your journal and task (graph sheets and responses), this comprises of
Part A, sections (6, 9-15)
Part B, section (4-6)
Part C, section (1-9)
Using the Random Sampler on the ABS Census at School
1. Go to the ABS census at School webpage. ( http://www.abs.gov.au/censusatschool)
2. Click on Random Sampler
3. Click accept.
4. Fill in relevant fields.
Ø Reference Year
Ø Questions to display
Ø Sample Size
Ø Sample characteristics
5. Click
6. You will now need to download the Excel file.
7. You should now have your data in an Excel file with 2 sheet tabs, it will look like this.
8. You are now ready to start working with the data
Marking Criteria - Yowie
Part A (11 marks) / MarkPrinted (two) data sets, indicating which pairs were eliminated and reasons
Printed two data sets, indicates no pairs were eliminated reason (all ok or similar)
Printed two data sets, indicates no pairs were eliminated / 2
1 / / 2
Draws a line of best fit by eye, gradient & y intercept to 1 decimal place, equation
S = mH+ b
Or combinations of those below
Draws a line of best fit by eye,
gradient &
y intercept to 1 decimal place,
equation S = mH+ b / 4
1
1
1
1 / / 4
Appropriate comment on limitations of the model indicating issues at both extremes / / 1
Predict belly button height (h) / / 1
Predict its arm span (S). / / 1
Find height (H) from belly button height (h) H = 2.3h / / 1
Yowie weight Wt (kg) = 0.79 x (height in cm) – 44.9 / / 1
Part B ( 3 marks)
Downloaded (sample of 200), printed & graph labelled Raw Data Part B & Deletes invalid pairs in the data set and prints, labelled Graph Part B
Penalty for not completing labelling of both (-1)
Penalty for not completing graphing of both (-1) / 2 / / 2
Comment on correlation, type and approximate correlation coefficient / / 1
Part C ( 22 marks)
Appropriate scatter plot Part C Graph printed, suitable gridlines, maximum & minimum scale values / / 1
Determines values for the least squares line of fit all correct
mean (x), mean (y)
stdev (x) stdev(y) for both correct using excel stdev.s (1 each) OR
stdev (x) stdev(y) for both correct using excel stdev.p
m uses correct formula to evaluate gradient in excel or by hand
r uses correct formula to evaluate correlation coefficient in excel or by hand
b uses correct formula to evaluate y- intercept in excel or by hand / 1
2
1
1
1
1 / /6
Substitutes 2 independent values in equation, determine two points for the least squares line of fit. All correct
OR combinations of
Writes equation using correct variables
Substitutes 2 independent variable to determine dependent variables (2 points for plotting) OR
Substitutes 1 independent variable to determine dependent variables (1 point for plotting) / 1
2
1 / / 3
Graphs the points above / / 1
Uses graph to predict the height from 43cm foot / / 1
By how much would the yowies height increase if the foot length increases by 1 cm? (uses gradient) / / 1
Explains answer above. (Gradient units)
E.g. indicates or explains rate /cm or gradient of line / / 1
Determines percentage error, using precision 1cm & Concise discussion/compares correlation coefficient e.g. % error V small however, r = 0.4 low so poor reliability in prediction i.e. a significant variation in data to determine either variable from any given variable value
Or
Determines percentage error, using precision 1cm
Concise : discussion/compares correlation coefficient
% error V small however, r = 0.4 low so poor reliability in prediction i.e.` a significant variation in data to determine either variable from any given variable value
Or
Weak : discussion/compares correlation coefficient
/ 1
2
1 / /3
Uses model or graph (extrapolate) to predict new born Yowie height based on foot size of 5cm. / / 1
What limitations may exist for the least squares line of best fit?
Thorough discussion, both limit extremes appropriately and discusses insufficient yowie data.
Average discussion, both limit extremes appropriately and discusses above. 2 of 3 items ok
Poor discussion, both limit extremes appropriately and discusses above. 1 of 3 items ok
E.g. It assumes humans and yowies are similar. Human height growth is limited at age 20’s, but we don’t know when this occurs in yowies.
It would seem reasonable to assume newborns yowies may also have bigger foot sizes as (all) reports seem to indicate quite tall animals. Insufficient Yowie data to do any appropriate predictions. / 3
2
1 / / 3
Age of yowie in Part A question 14; height e.g. 135 cm hence 7 years old or 98 cm a quite young yowie say 2-3 years old / /1
Logbook
4-5 good entries
2-3 good or 5 average
2-3 average or 4 average or 5 poor
1 good or 1-3 average / 4
3
2
1 / /4
Total / /40
Teacher comments