Questions

ADVANCED MATHEMATICS
Statistics (Adv), S2 Interpretation and Bivariate Data (Adv) 1. Statistics, STD2 S1 2010 HSC 1 MC
Other Chart Types (Y12) The results of a survey are displayed in the dot plot.
Teacher: Sunita Lampinen What is the range of this data?
Exam Equivalent Time: 79.5 minutes (based on allocation of 1.5 minutes per mark)

S2 Interpretation and Bivariate Data

2% 4% 6% 8% 10% 12%
*Analytics based on the average (A) 7
contribution to the 2ADV/STD2
Classifying Data HSC exams over the past decade. (B) 8
Bar Charts and Histograms
Other Chart Types (C) 9
Summary Statistics - Box Plots (D) 10
Summary Statistics - No Graph
Bivariate Data Analysis
2. Statistics, STD2 S1 2009 HSC 2 MC
The step graph shows the charges for a carpark.
HISTORICAL CONTRIBUTION
S2 Interpretation and Bivariate Data is a Year 12 topic that didn't previously existed in the Advanced
course, although it has a decade long history in the Std2/Gen2 exam.
It provides an area where examiners can test common content between the Advanced and Standard 2
courses. The above bar chart shows the relative importance of the subtopics in past Std2/Gen2
exams.
S2 Interpretation and Bivariate Data has been split into six sub-topics for analysis which are listed in
the bar chart above.
This analysis looks at Other Chart Types (0.8%).

HSC ANALYSIS - What to expect and common pitfalls Maria enters the carpark at 10:10 am and exits at 1:30 pm.
Pareto Charts were not examined in 2021 or 2020 Advanced exams but their debut in the 2019 Std2 How much will she pay in charges?
HSC produced a "red flag" mean mark of 18%! We highly recommend revision of this and other EQ-
Bank examples. (A)

A good understanding of Stem & Leaf plots is recommended and more particularly Double Stem and (B)
Leaf plots. These have caused problems in the past and warrant attention. (C)
We believe it is unlikely that examiners will test Area charts within the new syllabus, but the generality (D)
of the syllabus wording mean we can't guarantee this. Our current stance is to therefore briefly cover
this graph type.
Other charts tested that students have answered well include pie charts, segregated bar charts, step
graphs and dot plots.
3. Statistics, STD2 S1 2004 HSC 8 MC 5. Statistics, STD2 S1 2012 HSC 1 MC
This sector graph shows the distribution of 116 prizes won by three schools: X, Y and Z.  RAP Data - Bottom 19%: School result (60%) was 6% below state average (66%)

A set of 15 scores is displayed in a stem-and-leaf plot.

What is the median of these scores?

(A) 7
(B) 8

How many prizes were won by School X? (C) 77

(A) 26 (D) 78

(B) 32
(C) 81
(D) 99

4. Statistics, 2ADV S2 SM-Bank 5 MC

The stem plot below shows the height, in centimetres, of 20 players in a junior football team.

key: 14|2 = 142 cm n = 20

14 2 2 4 7 8 8 9
15 0 0 1 2 5 5 6 8
16 0 1 1 2
17 9

A player with a height of 179 cm is considered an outlier because 179 cm is greater than
A. 162 cm
B. 169 cm
C. 173 cm
D. 175.5 cm
6. Statistics, STD2 S1 2012 HSC 7 MC 7. Statistics, STD2 S1 2006 HSC 4 MC
The Pi Company has two bakeries. The radar chart displays the monthly sales for the bakeries. A set of scores is displayed in a stem-and-leaf plot.

What is the median of this set of scores?

(A) 28
(B) 30
(C) 33
(D) 47

8. Statistics, STD2 S1 2008 HSC 3 MC

The stem-and-leaf plot represents the daily sales of soft drink from a vending machine.

If the range of sales is 43, what is the value of ?

What was the difference in sales in June between the two bakeries?
(A) $7.50
(B) $17.50
(C) $7500
(D) $17 500

(A)
(B)
(C)
(D)
9. Statistics, STD2 S1 2018 HSC 17 MC 10. Statistics, STD2 S1 2010 HSC 16 MC
The area chart shows the number of students involved in tennis or cricket at a school over a number This back-to-back stem-and-leaf plot displays the test results for a class of 26 students.
of years.

What is the median test result for the class?

(A)
(B)
(C)
In which year was the number of students involved in tennis equal to the number of students
involved in cricket? (D)
A. 2013
B. 2014 11. Statistics, STD2 S1 2006 HSC 8 MC
C. 2015 Which of these graphs best represents positively skewed data with the smaller standard deviation?
D. 2016
12. Statistics, STD2 S1 2018 HSC 6 MC 14. Statistics, STD2 S1 2015 HSC 19 MC
 RAP Data - Bottom 9%: School result (34%) was 9% below state average (43%)  RAP Data - Bottom 17%: School result (33%) was 6% below state average (39%)

A set of data is displayed in this dot plot. The table shows the life expectancy (expected remaining years of life) for females at selected ages in
the given periods of time.

In 1975, a 45‑year‑old female used the information in the table to calculate the age to which she was
Which of the following best describes this set of data? expected to live. Twenty years later she recalculated the age to which she was expected to live.

A. Symmetrical What is the difference between the two ages she calculated?

B. Positively skewed (A) 2.7 years

C. Negatively skewed (B) 3.1 years

D. Normally distributed (C) 3.7 years

(D) 5.8 years

13. Statistics, STD2 S1 SM-Bank 2 MC

The dot plots show the height of students in Year 9 and Year 12 in a school. They are drawn on the
same scale.

Which statement about the change in heights when comparing Y9 to Y12 is correct?
A. The mean increased and the standard deviation decreased.
B. The mean decreased and the standard deviation decreased.
C. The mean increased and the standard deviation increased.
D. The mean decreased and the standard deviation increased.
15. Statistics, STD2 S1 2010 HSC 21 MC 16. Statistics, STD2 S1 2019 HSC 10 MC
The area graph shows the cost and profits for a business over a period of time. A school collected data related to the reasons given by students for arriving late. The Pareto chart
shows the data collected.

The information in the area graph is then displayed as a line graph.

Which of the following line graphs best displays the data from the area graph?

What percentage of students gave the reason 'Train or bus delay'?

A.
B.
C.
D.
17. Statistics, STD2 S1 2009 HSC 24a 18. Statistics, 2ADV S2 2022 HSC 11
 Part i: RAP Data - Bottom 12%: School result (76%) was 8% below state average (84%) The table shows the types of customer complaints received by an online business in a month.

The diagram below shows a stem-and-leaf plot for 22 scores.

a. What are the values of and ? (2 marks)

i. What is the mode for this data? (1 mark)
b. The data from the table are shown in the following Pareto chart.
ii. What is the median for this data? (1 mark)

The manager will address 80% of the complaints.

Which types of complaints will the manager address? (1 mark)
19. Statistics, STD2 S1 2005 HSC 24d 20. Statistics, STD2 S1 2008 HSC 23e
The sector graph shows the proportion of people, as a percentage, living in each region of Sumcity. In a survey, 450 people were asked about their favourite takeaway food. The results are displayed in
There are 24 000 people living in the Eastern Suburbs. the bar graph.

How many people chose pizza as their favourite takeaway food? (2 marks)

21. Statistics, STD2 S1 2017 HSC 26f

 Part i: RAP Data - Bottom 22%: School result (50%) was 5% below state average (55%)
 Part ii: RAP Data - Bottom 10%: School result (64%) was 9% below state average (73%)

The area chart shows the number of goals scored by three hockey teams, , and , in the first 4
rounds.
i. Show that the total number of people living in Sumcity is 160 000. (1 mark)

Jake used the information above to draw a column graph. 10

9
8
7

Goals scored
6 C
5 B
4
3 A
2
1
0
Round 1 Round 2 Round 3 Round 4

i. How many goals were scored by team in round 1? (1 mark)

ii. The column graph height is incorrect for one region. ii. In which round did all three teams score the same number of goals? (1 mark)

Identify this region and justify your answer. (2 marks)

22. Statistics, STD2 S1 2007 HSC 24d 23. Statistics, STD2 S1 2011 HSC 25d
Barry constructed a back-to-back stem-and-leaf plot to compare the ages of his students.  Part i: RAP Data - Bottom 12%: School result (60%) was 8% below state average (68%)

Data was collected from 30 students on the number of text messages they had sent in the previous
24 hours. The set of data collected is displayed.

i. Write a brief statement that compares the distribution of the ages of males and females from this
set of data. (1 mark)
ii. What is the mode of this set of data? (1 mark)

iii. Liam decided to use a grouped frequency distribution table to calculate the mean age of the
students at Barry’s Ballroom Dancing Studio. i. What is the outlier for this set of data? (1 mark)
For the age group 30 - 39 years, what is the value of the product of the class centre and the ii. What is the interquartile range of the data collected from the female students? (1 mark)
frequency? (2 marks)
iv. Liam correctly calculated the mean from the grouped frequency distribution table to be 39.5. 24. Statistics, STD2 S1 2005 HSC 24a
Caitlyn correctly used the original data in the back-to-back stem-and-leaf plot and calculated the
mean to be 38.2. i. Draw a stem-and-leaf plot for the following set of scores.
What is the reason for the difference in the two answers? (1 mark) (2 marks)

ii. What is the median of the set of scores? (1 mark)

iii. Comment on the skewness of the set of scores. (1 mark)

25. Statistics, STD2 S1 EQ-Bank 4 26. Statistics, STD2 S1 2013 HSC 26f
A high school conducted a survey asking students what their favourite Summer sport was. Jason travels to work by car on all five days of his working week, leaving home at 7 am each day. He
compares his travel times using roads without tolls and roads with tolls over a period of 12 working
The Pareto chart shows the data collected.
weeks.
He records his travel times (in minutes) in a back-to-back stem-and-leaf plot.

i. What is the modal travel time when he uses roads without tolls? (1 mark)

ii. What is the median travel time when he uses roads without tolls? (1 mark)

iii. Describe how the two data sets differ in terms of the spread and skewness of their distributions. (2
marks)

27. Statistics, STD2 S1 2016 HSC 29c

i. What percentage of students chose Hockey as their favourite Summer sport? (1 mark)
The ages of members of a dance class are shown in the back-to-back stem-and-leaf plot.
ii. What percentage of students chose Touch Football as their favourite Summer sport? (1 mark)

Pat claims that the women who attend the dance class are generally older than the men.
Is Pat correct? Justify your answer by referring to the median and skewness of the two sets of data.
(3 marks)
28. Statistics, STD2 S1 EQ-Bank 5 29. Statistics, STD2 S1 EQ-Bank 6
An island resort surveyed 400 guests by asking them on which continent they lived. The Pareto chart below shows the data collected from a survey where people were asked to choose
their favourite overseas holiday destination.
The table below shows the data collected.
Using the chart, how many people were surveyed? (2 marks)

Complete the Pareto chart below to show the data collected. (3 marks)

Copyright © 2004-22 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW)
Worked Solutions 6. Statistics, STD2 S1 2012 HSC 7 MC

1. Statistics, STD2 S1 2010 HSC 1 MC

7. Statistics, STD2 S1 2006 HSC 4 MC

2. Statistics, STD2 S1 2009 HSC 2 MC

3. Statistics, STD2 S1 2004 HSC 8 MC

8. Statistics, STD2 S1 2008 HSC 3 MC

9. Statistics, STD2 S1 2018 HSC 17 MC

4. Statistics, 2ADV S2 SM-Bank 5 MC

10. Statistics, STD2 S1 2010 HSC 16 MC

♦♦ Mean mark 35%

5. Statistics, STD2 S1 2012 HSC 1 MC

11. Statistics, STD2 S1 2006 HSC 8 MC 16. Statistics, STD2 S1 2019 HSC 10 MC

♦♦♦ Mean mark 18%.

17. Statistics, STD2 S1 2009 HSC 24a

i.

12. Statistics, STD2 S1 2018 HSC 6 MC ii.

♦ Mean mark 43% (a surprisingly

poor result!)

13. Statistics, STD2 S1 SM-Bank 2 MC

18. Statistics, 2ADV S2 2022 HSC 11
a.

14. Statistics, STD2 S1 2015 HSC 19 MC

b.

♦ Mean mark 39%.

15. Statistics, STD2 S1 2010 HSC 21 MC

♦♦♦ Mean mark 24%

COMMENT: Area graph questions
have proven very challenging over
recent years. Review this area.
19. Statistics, STD2 S1 2005 HSC 24d 22. Statistics, STD2 S1 2007 HSC 24d
i. i.

ii. ii.

iii.

20. Statistics, STD2 S1 2008 HSC 23e

COMMENT: This question required

measurement of the actual image
on the exam. The same
methodology works here.
iv.

21. Statistics, STD2 S1 2017 HSC 26f 23. Statistics, STD2 S1 2011 HSC 25d
i.
i.
ii.
♦♦ Mean mark 34%
COMMENT: Ensure you can
quickly and accurately find quartile
values using stem and leaf graphs!
ii.
24. Statistics, STD2 S1 2005 HSC 24a 26. Statistics, STD2 S1 2013 HSC 26f

i. i.

♦ Mean mark 36%

MARKER’S COMMENT: Finding a
ii.
median proved challenging for
many students. Take note!

ii.

♦ Mean mark 39%

iii.

iii.

25. Statistics, STD2 S1 EQ-Bank 4 27. Statistics, STD2 S1 2016 HSC 29c
i.
♦ Mean mark 44%.

ii.
28. Statistics, STD2 S1 EQ-Bank 5

29. Statistics, STD2 S1 EQ-Bank 6

Copyright © 2016-2023 M2 Mathematics Pty Ltd (SmarterMaths.com.au)