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Year 10 Mathematics
Item number:
2, Semester 1, 2015
Item type:
Investigation
Topics covered: Statistics and Probability – Data representation and interpretation
Time:
4 weeks (including 2 class lessons)
Name:
PC Class
Subject teacher:
Mr Hughes
Mr O’Sullivan
Miss Rogers
Date completed:
Results:
Dimension
A
B
C
D
E
Understanding
Skills
Assignment lesson(s): Wednesday, May 6th and Thursday May 14th
Students who miss these lessons due to other commitments or illness should not expect to be
granted additional assignment lessons (subject to the assessment policy)
Monitoring date: Thursday May 14th
Students are required to show their teacher a work in progress on or before this date.
Draft deadline: Wednesday May 13th
An optional draft may be submitted by this deadline. Teachers may accept drafts after this
deadline though no guarantee is given that the draft will be reviewed in time for students to receive
feedback.
Declaration of originality
I declare that the work presented in my response is my own, original work except where indicated.
I understand there are consequences for plagiarism as outlined in the school assessment and
behaviour management policies.
Signed: ______________________
Date: ______________
Guide to making judgements
Understanding
Skills
Uses evidence to draw conclusions, establish trends and make predictions,
explains choices and strategies.
Performs calculations involving measures of central tendency and spread,
including IQR, displays data using appropriate displays, and communicates
mathematically.
Data analysis provides clear evidence the student has interpreted the
summary statistics and data displays correctly. The discussions and
conclusions are detailed, insightful and directly relate to statistical evidence
presented.
Accurate and efficient use of mathematical procedures and calculations to find
solutions; accurately collects and displays information using appropriate
graphical displays; accurate and clear communication using appropriate
mathematical language, conventions and symbols.
A
B
Data analysis is basic and is mostly limited to a restatement of the statistical
measures presented. The discussion and conclusion relates to statistical
evidence presented. The student has addressed some aspects of tasks 2 – 4.
Appropriate use of mathematical procedures and calculations to find solutions;
collects and displays information in graphical form; communication using
appropriate mathematical language, conventions and symbols.
Use of simple mathematical procedures; communication using aspects of
mathematical language, conventions and symbols.
Data analysis is missing or limited to a restatement of some aspects of the
student’s calculation. Discussion shows very limited understanding of the
information displayed in a boxplot.
C
D
E
Instructions:
•
•
•
You may choose to complete either section A or section B of this assignment
Your response is to be completed on separate paper and attached to this task sheet for
submission.
Do not place your response in a plastic sleeve or folder.
Assessment Policy
Please refer to the assessment procedures for Years 7-12 in the student diary. This contains
important information regarding drafts, extensions and due dates.
Advice on which section to complete
Section A
Students who submit a perfect response to Section A can achieve, at most, an “A” for this
assessment piece.
Section B
Students who complete a high-quality response to Section B can achieve an “A+” for this
assessment piece. Section B must be completed as part of a team.
Q:\Maths\02 - Assessment\Year 10\2015\Item 2\Item 2 - Statistics Assignment.docx
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SECTION A
Task 1 (Skills C, Understanding C)
Two classes of students underwent a fitness test and their results are given below.
Note: The higher the score, the fitter the student.
Class A
5.0
5.4
12.2
Class B
6.2
12.6
6.8
14.2
6.2
15.0
7.4
14.2
7.4
15.0
7.4
14.2
8.0
16.2
8.2
14.6
8.2
16.4
9.0
15.2
8.2
18.0
10.2
16.2
9.2
18.0
10.4
16.8
9.8
18.2
10.6
17.0
10.4
19.0
10.6
18.2
10.6
22.6
12.2
18.8
10.6
24
12.2
20.2
10.6
14.0
20.8
a) Construct a pair of parallel boxplots displaying the results above.
b) With specific reference to median, minimum, maximum and inter-quartile range, compare the
classes (write at least 3 sentences that describe the data).
Task 2 (Skills C/B, Understanding B)
A prominent exercise scientist claims that there is a relationship between a person’s arm span and
their potential as a swimmer. Specifically, she believes that the greater the arm span/height ratio
is, the faster they will be able to swim.
For example:
Michael Phelps is 193cm tall, has an arm span of 200cm and his personal best for the 100m
freestyle is 46.65 seconds. The relevant data is summarised below.
Arm span / height ratio
200 ÷ 193 = 1 .0363
100m freestyle time
46.65
Below are the arm span, height and personal best times for 10 nationally ranked swimmers who
are at (or are close to) the peak of their ability.
Name
J Armstrong
P Smith
K Matthews
L Nelson
D Harris
M Robinson
H Mick
S Morrison
T Burton
L Lanzon
Arm span (cm)
189
191
190
185
179
186
178
183
198
180
Height (cm)
184
186
190
180
182
185
175
184
191
182
Q:\Maths\02 - Assessment\Year 10\2015\Item 2\Item 2 - Statistics Assignment.docx
100m freestyle time
47.82 s
47.99 s
52.14 s
47.14 s
54.02 s
49.10 s
48.50 s
52.04 s
48.12 s
52.61 s
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SECTION A
Task 2 continued
a) Find the arm span / height ratio for each swimmer
b) Construct a scatterplot of best time vs ratio and decide if you support the scientist’s theory.
Ensure the independent variable is on the horizontal axis.
c) If a relationship does exist, manually determine the equation of the relationship
d) If a relationship does exist, use Microsoft excel to determine the equation of the trend line, and
thus verify your answer to Task 2c.
Task 3 (Skills B, Understanding A)
Consider all the data from Task 1 (both classes). For this fitness test, a student would be
considered a truly exceptional athlete if they scored greater than 3 standard deviations above the
mean. Based on the test scores, are there any students who would be considered truly
exceptional?
Task 4 – Research Task (Skills B, Understanding A)
Note: A high degree of initiative is intended for this task. Your teacher is permitted to help you
understand the concept of “skewness” but cannot help you complete the task otherwise.
Part A) Research the concept of “skewness” as presented on page 459 – 461 of your textbook.
Part B) Collect data relating to the heights of students in year 10 at St Luke’s. Your data must be
representative of the group and your response should include a description of how you achieved
this.
Part C) With appropriate evidence, discuss the distribution of heights of students in Year 10.
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SECTION B
Research and analysis task
Task brief
Statistics provides efficient methods of collecting, analysing and displaying data. It is often
essential in identifying patterns and associations. Business, corporations and governments rely on
statistics to inform decision making.
Working in a team of your choice, you are to investigate a topic of interest. You will collect,
analyse and display data regarding this topic, and present your findings as a research report.
As this task is primarily a demonstration of what you have learned about statistics, the topic
selected should allow you to compare and analyse at least two datasets.
If you select to respond to this task, it is highly recommended you attempt to include evidence that
you have satisfied learning goals from the “Working above year level” column on the 2nd page of
your statistics workbook.
For this reason certain types of investigations would not be appropriate. Collecting data on what
types of food people prefer to purchase at the tuckshop, or looking at the most popular car colours
are examples of topics that would not allow you to demonstrate your ability.
Presentation
Each student in the team will submit a report which contains:
•
•
•
•
•
•
•
A summary of the investigation, including objective, research question and method of data
collection
Evidence of data collected (tally sheets, frequency tables etc)
Collected data displayed in appropriate ways
Calculations of various statistical methods
A detailed analysis of the data you have collected.
A discussion of findings including conclusions, predictions (if appropriate) and
recommendations
A discussion on whether enough data has been collected to ensure conclusions are valid
and any possible improvements that could be made
Planning your experiment/investigation
This task allows you and your team mates to work independently of your teacher and create
something truly impressive. However, you must communicate certain things to your teacher along
the way.
On the next page is a series of steps to help you plan out your experiment/investigation, and keep
your teacher in the loop as well.
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SECTION B
Choose a partner and topic
a) Choose your team mates carefully; make sure they are people you trust to do their fair share of
the work. You are permitted to choose team mates from other classes.
b) Put some real thought into your topic. Make sure you have read the task brief regarding what
you need to demonstrate in this task.
Your teacher must approve your team member(s) and topic by: _________________
negotiated date
Establish what you intend to investigate
You are to provide a summary of the investigation you intend to carry out. This summary must
include:
•
•
•
An objective (what are you trying to find out?)
The means by which you will collect information
A statement addressing how you will avoid bias in your data collection
Your teacher must view the investigation summary by: _________________
negotiated date
Collect the data
Each student must submit evidence of data collection. The format of this will depend on the data
you have collected but might include completed questionnaires, tally sheets or frequency tables.
Your teacher must site evidence of data collection by: _________________
negotiated date
Analyse the data
Each student must be involved in calculating measures of central tendency and spread, and
creating data displays such as scatterplots and boxplots. Be sure to read the task brief and reflect
on what you wrote in your investigation summary.
The data analysis should not only consist of calculations and graphs. It should be based on the
evidence obtained from the statistical measures calculated and should also contain:
•
•
•
•
Insightful discussion of any interesting findings or trends
If appropriate, comparison of different datasets
If appropriate, predictions based on evidence
A conclusion as to whether you met the objective you set out to achieve
Submit a draft of your analysis to your teacher by: _________________
negotiated date
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