VCE General Maths Data Analysis 2020 Mini Test 1

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.

Data analysis - 2020 - Exam 2 (Part 1)

Question 1 (5 marks) [2020 Exam 2 Q2]

The neck size, in centimetres, of 250 men was recorded and displayed in the dot plot below.

A dot plot showing the neck size (in cm) of 250 men. The x-axis ranges from 30 to 45. The distribution is approximately symmetric and bell-shaped, centered around 38. The frequency is highest at 38 cm and decreases on either side.

a. Write down the modal neck size, in centimetres, for these 250 men. 1 mark

b. Assume that this sample of 250 men has been drawn at random from a population of men whose neck size is normally distributed with a mean of 38 cm and a standard deviation of 2.3 cm.

i. How many of these 250 men are expected to have a neck size that is more than three standard deviations above or below the mean?
Round your answer to the nearest whole number. 1 mark

ii. How many of these 250 men actually have a neck size that is more than three standard deviations above or below the mean? 1 mark

c. The five-number summary for this sample of neck sizes, in centimetres, is given below.

Minimum First quartile (\(Q_1\)) Median Third quartile (\(Q_3\)) Maximum
31 36 38 39 44

Use the five-number summary to construct a boxplot, showing any outliers if appropriate, on the grid below. 2 marks

A grid for constructing a boxplot. The x-axis is labelled 'neck size (cm)' and ranges from 30 to 45.
Question 2 (5 marks) [2020 Exam 2 Q3]

In a study of the association between BMI and neck size, 250 men were grouped by neck size (below average, average and above average) and their BMI recorded. Five-number summaries describing the distribution of BMI for each group are displayed in the table below along with the group size. The associated boxplots are shown below the table.

Neck size Group size BMI (kg/m²)
Min. \(Q_1\) Median \(Q_3\) Max.
below average 50 18.1 20.6 21.6 23.2 26.8
average 124 19.8 23.4 24.6 26.0 33.9
above average 76 23.1 26.25 28.1 29.95 39.1
A table showing five-number summaries for BMI grouped by neck size (below average, average, above average) and parallel boxplots illustrating this data. The table shows that as neck size increases from below average to above average, the median BMI also increases (21.6, 24.6, 28.1). The boxplots visually confirm this positive association, with the boxes for each group shifting to higher BMI values. The 'above average' group also shows several outliers at the higher end.

a. What percentage of these 250 men are classified as having a below average neck size? 1 mark

b. What is the interquartile range (IQR) of BMI for the men with an average neck size? 1 mark

c. People with a BMI of 30 or more are classified as being obese.
Using this criterion, how many of these 250 men would be classified as obese? Assume that the BMI values were all rounded to one decimal place. 1 mark

d. Do the boxplots support the contention that BMI is associated with neck size? Refer to the values of an appropriate statistic in your response. 2 marks

End of Multiple-Choice Question Book

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