VCE General Maths Data Analysis 2024 Mini Test 2

VCAA General Maths Exam 2

This is the full VCE General Maths Exam with worked solutions. You can also try Mini-Tests, which are official VCAA exams split into short tests you can do anytime.

Number of marks: 10

Reading time: 2.5 minutes

Writing time: 15 minutes

Formula Sheet 
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Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In all questions where a numerical answer is required, you should only round your answer when instructed to do so.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.

VCE Maths Topic Questions

Data analysis - 2024 - Exam 2 (Part 2)

Question 1 (10 marks) [2024 Exam 2 Q3]

The Olympic gold medal-winning height for the women’s high jump, \(Wgold\), is often lower than the best height achieved in other international women’s high jump competitions in that same year.

Table 2 lists the Olympic year, year, the gold medal-winning height, \(Wgold\), in metres, and the best height achieved in all international women’s high jump competitions in that same year, \(Wbest\), in metres, for each Olympic year from 1972 to 2020.

Table 2

year 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020
Wgold (m) 1.92 1.93 1.97 2.02 2.03 2.02 2.05 2.01 2.06 2.05 2.05 1.97 2.04
Wbest (m) 1.94 1.96 1.98 2.07 2.07 2.05 2.05 2.02 2.06 2.06 2.05 2.01 2.05

A scatterplot of \(Wbest\) versus \(Wgold\) for this data is also provided.


A scatterplot of Wbest (m) vs Wgold (m). The x-axis (Wgold) ranges from 1.90 to 2.08. The y-axis (Wbest) ranges from 1.92 to 2.10. Data points show a positive association.

When a least squares line is fitted to the scatterplot, the equation is found to be:

\(Wbest = 0.300 + 0.860 \times Wgold\)

The correlation coefficient is 0.9318

a. Name the response variable in this equation. 1 mark

b. Draw the least squares line on the scatterplot above. 1 mark

c. Determine the value of the coefficient of determination as a percentage.
Round your answer to one decimal place. 1 mark

d. Describe the association between \(Wbest\) and \(Wgold\) in terms of strength and direction. 1 mark

strength
direction<

e. Referring to the equation of the least squares line, interpret the value of the slope in terms of the variables \(Wbest\) and \(Wgold\). 1 mark

f. In 1984, the \(Wbest\) value was 2.07 m for a \(Wgold\) value of 2.02 m.
Show that when this least squares line is fitted to the scatterplot, the residual value for this point is 0.0328 2 marks

g. The residual plot obtained when the least squares line was fitted to the data is shown below. The residual value from part f is missing from the residual plot.

A residual plot with Wgold (m) on the x-axis from 1.90 to 2.08, and residual on the y-axis from -0.02 to 0.04. The points are scattered randomly around the zero line.

i. Complete the residual plot by adding the residual value from part f, drawn as a cross (X), to the residual plot above. 1 mark

ii. In part b, a least squares line was fitted to the scatterplot.
Does the residual plot from part g justify this? Briefly explain your answer. 1 mark

h. In 1964, the gold medal-winning height, \(Wgold\), was 1.90 m. When the least squares line is used to predict \(Wbest\), it is found to be 1.934 m.
Explain why this prediction is not likely to be reliable. 1 mark

End of Multiple-Choice Question Book

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