WORKSHEET General 2 Mathematics Topic Areas: FOCUS STUDIES Mathematics and Health Correlation / Body Measurements Life Expectancy Medication Teacher: PETER HARGRAVES Source: HSC exam questions Exam Equivalent Time: 55.5 minutes Worked Solutions: Included Note: Each question has designated marks. Use this information as both a guide to the question's difficulty and as a timing indicator, whereby each mark should equate to 1.5 minutes of working (examination) time. Questions 1. FS Health, 2011 HSC 8 MC In which graph would the data have a correlation coefficient closest to
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WORKSHEET General 2 MathematicsTopic Areas:FOCUS STUDIES
Mathematics and Health Correlation / Body Measurements Life Expectancy Medication
Teacher: PETER HARGRAVESSource: HSC exam questionsExam Equivalent Time: 55.5 minutesWorked Solutions: IncludedNote: Each question has designated marks. Use this information as both a guide to the question's difficultyand as a timing indicator, whereby each mark should equate to 1.5 minutes of working (examination) time.
Questions
1. FS Health, 2011 HSC 8 MC
In which graph would the data have a correlation coefficient closest to – 0.9?
Which of the following best describes the correlation between and ?
(A) Positive
(B) Negative
(C) Positively skewed
(D) Negatively skewed
5. FS Health, 2UG 2014 HSC 4 MC
Young’s formula below is used to calculate the required dosages of medicine for children aged years.
How much of the medicine should be given to an monthold child in a hour period ifeach adult dosage is mL? The medicine is to be taken every hours by both adults andchildren.
Tony sees an eruption that lasts minutes. Based on the data in the graph, what isthe minimum time that he can expect to wait for the next eruption? (1 mark)Julia saw two consecutive eruptions, one hour apart. Based on the data in thegraph, what was the longest possible duration of the first eruption that she saw? (1mark)What does the graph suggest about the relationship between the duration of aneruption and the time to the next eruption? (1 mark)
8. Data, 2UG 2012 HSC 29a
Tourists visit a park where steam erupts from a particular geyser.
The brochure for the park has a graph of the data collected for this geyser over a period oftime.
The graph shows the duration of an eruption and the time until the next eruption, timed fromthe end of one eruption to the beginning of the next.
(i)
(ii)
(iii)
(NB. Changes in the Syllabus now have correlation in the Focus Study:Health category and hence this question is classified twice, under"Data" and "FS Health")
9. FS Health, 2UG Med S2
A medication is available in both tablet and liquid form. A tablet contains of the activeingredient while the liquid form contains per . Michael likes taking tablets andGeorgia prefers liquid medicines. If they each need of the active ingredient, whatdosages do they take? (3 marks)
The expenditures per primary school student for the countries in the scatterplotare:
For the given data, the correlation coefficient, , is . What does this indicateabout the relationship between expenditure per primary school student and lifeexpectancy for the countries? (1 mark)
For the data representing expenditure per primary school student, is and is .What is the interquartile range? (1 mark)
Another country has an expenditure per primary school student of of itsGDP. Would this country be an outlier for this set of data? Justify your answer withcalculations. (2 marks)
Complete the table below by calculating the mean, , and the standard deviation,
, of these data. Calculate both values to two decimal places.
The table also shows the mean, , and the standard deviation, , oflife expectancy for the same countries. (2 marks)
percentage of a country’s Gross Domestic Product (GDP), and the life expectancy in years for countries.
♦♦ Mean marks of 38%, 26%and 25% respectively for parts(i)(iii).MARKER'SCOMMENT: Interpretinggradients has been consistentlyexamined in recent history andalmost always poorlyanswered. Work hard tounderstand this area.
♦♦ Mean mark 30%Note that the Formulae andData Sheet gives you thegradient and interceptformulae you need for thisquestion.
♦♦ Mean mark 32%Only a minority of studentscould draw the line of best fit onthe graph. This can simply bedone using 2 points the intercept (49.9) and another onechosen.
(iv)
(v)
(vi)
Need to show y = 1.29x + 49.9
y
Gradient = r ×σy
σx
= 0.83 ×10.947.03
= 1.2916...
= 1.29 (2 d.p.)
y intercept = − (gradient × )y x
= 70.73 − (1.29 × 16.14)
= 49.909...
= 49.9 (1 d.p.)∴ y = 1.29x + 49.9 ... as required.
♦♦♦ Mean mark 0%. Thetoughest question on the 2014paper.COMMENT: Examiners oftenlike to highlight linearrelationships that only work in agiven range and have studentscomment on outliers where therelationship breaks down.