Analyze and Present Research Conclusions
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AI Summary
This assignment requires you to critically analyze research conclusions, ensuring they are valid and supported by adequate evidence. You will need to evaluate the use of academic conventions, including referencing and argumentation, in presenting these conclusions. The task involves developing strong conclusions based on a satisfactory range of relevant literature, while also demonstrating good academic skills.
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Learning outcomes assessed:
Apply numerical skills, concepts and techniques in a variety of
business and academic contexts.
Demonstrate an ability to calculate and interpret statistical values.
Be able to interpret and process mathematical problems in personal
and professional contexts.
This coursework is worth 100% of the total marks for this module.
Apply numerical skills, concepts and techniques in a variety of
business and academic contexts.
Demonstrate an ability to calculate and interpret statistical values.
Be able to interpret and process mathematical problems in personal
and professional contexts.
This coursework is worth 100% of the total marks for this module.
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
Coursework Instructions
Please read carefully
• Carefully read the module handbook, the marking criteria and the
grade descriptors.
Academic Misconduct
You are responsible for ensuring you understand the policy and
regulations about academic misconduct. You must:
• Complete this work alone except where required or allowed by this
assignment briefing paper and ensure it has not been written or
composed by or with the assistance of any other person.
• Make sure all sentences or passages quoted from other people’s
work in this assignment (with or without trivial changes) are in
quotation marks, and are specifically acknowledged by reference
to the author, work and page.
This portfolio consists of four sections:
Sections 1, 2 and 3 are assessed in ‘pass/fail’ criteria. Sections 1, 2
and 3 combined are worth 45% of the final mark.
For example, if a student completes and passes 5 out of 9 tasks
outlined in Sections 1, 2 and 3 he/she will be given the following
marks:
5 / 9 x 45 = 25
Sections 1, 2 and 3 each consist of 3 tasks:
Task 1 – Skills Audit
Task 2 – In class Activity
Task 3 – Online Activity - students are expected to complete and pass
(40%) relevant online activity/quiz. The results page will need to be
saved (screenshot) and inserted under a relevant area of the
portfolio.
Coursework Instructions
Please read carefully
• Carefully read the module handbook, the marking criteria and the
grade descriptors.
Academic Misconduct
You are responsible for ensuring you understand the policy and
regulations about academic misconduct. You must:
• Complete this work alone except where required or allowed by this
assignment briefing paper and ensure it has not been written or
composed by or with the assistance of any other person.
• Make sure all sentences or passages quoted from other people’s
work in this assignment (with or without trivial changes) are in
quotation marks, and are specifically acknowledged by reference
to the author, work and page.
This portfolio consists of four sections:
Sections 1, 2 and 3 are assessed in ‘pass/fail’ criteria. Sections 1, 2
and 3 combined are worth 45% of the final mark.
For example, if a student completes and passes 5 out of 9 tasks
outlined in Sections 1, 2 and 3 he/she will be given the following
marks:
5 / 9 x 45 = 25
Sections 1, 2 and 3 each consist of 3 tasks:
Task 1 – Skills Audit
Task 2 – In class Activity
Task 3 – Online Activity - students are expected to complete and pass
(40%) relevant online activity/quiz. The results page will need to be
saved (screenshot) and inserted under a relevant area of the
portfolio.
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Section 4 is worth 55% of the final mark and consists of 10 questions.
Students are required to complete all questions and tasks set
out in this portfolio.
Task 1 Task 2 Task 3 Total
Par
t
1
Section 1 Pass/Fail
(Skills Audit)
Pass/Fail
(In class
activity)
Pass/Fail
(Online
Activity)
45 %
Section 2 Pass/Fail
(Skills Audit)
Pass/Fail
(In class
activity)
Pass/Fail
(Online
Activity)
Section 3 Pass/Fail
(Skills Audit)
Pass/Fail
(In class
activity)
Pass/Fail
(Online
Activity)
Part
2 Section 4
55%
(10
questions)
N/A N/A 55%
100%
Section 4 is worth 55% of the final mark and consists of 10 questions.
Students are required to complete all questions and tasks set
out in this portfolio.
Task 1 Task 2 Task 3 Total
Par
t
1
Section 1 Pass/Fail
(Skills Audit)
Pass/Fail
(In class
activity)
Pass/Fail
(Online
Activity)
45 %
Section 2 Pass/Fail
(Skills Audit)
Pass/Fail
(In class
activity)
Pass/Fail
(Online
Activity)
Section 3 Pass/Fail
(Skills Audit)
Pass/Fail
(In class
activity)
Pass/Fail
(Online
Activity)
Part
2 Section 4
55%
(10
questions)
N/A N/A 55%
100%
MATI3006- Numeracy1 Summer 2017 Coursework Brief
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
SECTION 1
This section will focus on order of operations (BODMAS); operations on
positive and negative numbers; fractions and ratios.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your
answers should show good reflection and awareness of your
strengths and areas for improvement.
I know how to…. I can
do well
I need
practic
e
I’m not
sure
I can’t
do
11 I know what BODMAS stands for. ☒ ☐ ☐ ☐
11 I can apply BODMAS to a variety of
calculations.
☒ ☐ ☐ ☐
11 I can define a fraction, numerator
and denominator.
☒ ☐ ☐ ☐
11 I can define proper fraction,
improper fraction and a mixed
number.
☒ ☐ ☐ ☐
11 I can convert a mixed number to
an improper fraction.
☒ ☐ ☐ ☐
11 I can convert improper fraction to a
mixed number.
☒ ☐ ☐ ☐
11 I can add, subtract, multiply and
divide fractions.
☒ ☐ ☐ ☐
11 I can explain the meaning of a
ratio.
☒ ☐ ☐ ☐
11 I can work with simple ratios. ☒ ☐ ☐ ☐
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal
learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also
consider the following points:
Reflect on your learning
How did you contribute in the class?
What went well?
Are there any areas for improvement?
SECTION 1
This section will focus on order of operations (BODMAS); operations on
positive and negative numbers; fractions and ratios.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your
answers should show good reflection and awareness of your
strengths and areas for improvement.
I know how to…. I can
do well
I need
practic
e
I’m not
sure
I can’t
do
11 I know what BODMAS stands for. ☒ ☐ ☐ ☐
11 I can apply BODMAS to a variety of
calculations.
☒ ☐ ☐ ☐
11 I can define a fraction, numerator
and denominator.
☒ ☐ ☐ ☐
11 I can define proper fraction,
improper fraction and a mixed
number.
☒ ☐ ☐ ☐
11 I can convert a mixed number to
an improper fraction.
☒ ☐ ☐ ☐
11 I can convert improper fraction to a
mixed number.
☒ ☐ ☐ ☐
11 I can add, subtract, multiply and
divide fractions.
☒ ☐ ☐ ☐
11 I can explain the meaning of a
ratio.
☒ ☐ ☐ ☐
11 I can work with simple ratios. ☒ ☐ ☐ ☐
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal
learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also
consider the following points:
Reflect on your learning
How did you contribute in the class?
What went well?
Are there any areas for improvement?
MATI3006- Numeracy1 Summer 2017 Coursework Brief
QUESTION 2
Give one example of a ‘real-life’ problem or situation that involves one (or
more) of the following topics:
Order of operations
Operations on positive and negative numbers
Fractions
Ratios
Also, please find a solution to the problem you described.
Order of operations (BODMAS)
Order of operations (BODMAS) can be simply defined as the ways through
which the calculations related with mathematics are solved. BODMAS stands for
Brackets, Order, Division, Multiplication, Addition and Subtraction (Circelli and et. al.,
2012). Any calculation is solved by using the priority that is explained below:
Brackets > Of > Division > Multiplication > Addition > Subtraction
For example if any mathematical problem is like 7 + (5^2 * 6 + 3), then the order of
operations is like this:
Brackets is solved first as follow:
First step: 6 * (5 + 3) = 6 * 8 = 48 (Correct)
6 * (5 + 3) = 30 + 3 = 33 (wrong)
Then exponents ( power , roots) is solved before multiply, divide, add or subtract.
Second step: 5 * 2^2= 5 * 4 = 20 (correct)
5 * 2^2 =10^2 = 100 (wrong)
Then multiplication or division is performed before addition or subtraction
Third step: 2+ 5 * 3 = 2 + 15 = 17 (correct)
2 + 5 * 3 = 7 * 3 = 21 (wrong)
Otherwise just going left to right
Fourth step : 30 / 5 + 3 = 6 * 3 = 18 (correct)
30 / 5 * 3 = 30 / 15 = 2 (wrong)
Note: B Brackets first
O Orders ( that is power and square roots, etc.)
DM Division and Multiplication (Left to right)
AS Addition and Subtraction (left to right)
QUESTION 2
Give one example of a ‘real-life’ problem or situation that involves one (or
more) of the following topics:
Order of operations
Operations on positive and negative numbers
Fractions
Ratios
Also, please find a solution to the problem you described.
Order of operations (BODMAS)
Order of operations (BODMAS) can be simply defined as the ways through
which the calculations related with mathematics are solved. BODMAS stands for
Brackets, Order, Division, Multiplication, Addition and Subtraction (Circelli and et. al.,
2012). Any calculation is solved by using the priority that is explained below:
Brackets > Of > Division > Multiplication > Addition > Subtraction
For example if any mathematical problem is like 7 + (5^2 * 6 + 3), then the order of
operations is like this:
Brackets is solved first as follow:
First step: 6 * (5 + 3) = 6 * 8 = 48 (Correct)
6 * (5 + 3) = 30 + 3 = 33 (wrong)
Then exponents ( power , roots) is solved before multiply, divide, add or subtract.
Second step: 5 * 2^2= 5 * 4 = 20 (correct)
5 * 2^2 =10^2 = 100 (wrong)
Then multiplication or division is performed before addition or subtraction
Third step: 2+ 5 * 3 = 2 + 15 = 17 (correct)
2 + 5 * 3 = 7 * 3 = 21 (wrong)
Otherwise just going left to right
Fourth step : 30 / 5 + 3 = 6 * 3 = 18 (correct)
30 / 5 * 3 = 30 / 15 = 2 (wrong)
Note: B Brackets first
O Orders ( that is power and square roots, etc.)
DM Division and Multiplication (Left to right)
AS Addition and Subtraction (left to right)
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
Operations on positive and negative numbers
There are four operations that are applied on positive and negative numbers that
are listed below:
1. Additive rules:
When two positive numbers are added then the result will also positive (i.e.
positive + positive = positive) . For example : 5 +2 = 7.
When two negative numbers are added then the output will also negative. (i.e.
Negative + Negative = Negative). For example: (-7) + ( -5) = -12
Sum of negative and positive number: Here sign of larger number is taken and
subtraction operation is carried on. Example: (-6) +4 = -10.
2. Subtracting rules :
Negative - positive = Negative. e.g. (-5) - (-4) = -5 + 4 = -9.
Positive - Negative = Positive + Positive = Positive. e.g. 5- (-4) = 5 + 4 = 9.
Negative - Negative = Negative + Positive = Here sign of larger number and
subtraction is performed. e.g. (-6) - (-7) = (-6) + 7 = -1; (-3) - (-6) = (-3) + 6 = 3,
etc.
3. Multiplying rules:
Positive * Positive = Positive. e.g. 4 * 5= 20.
Negative * Negative = Negative. e.g. (-3) * (-2) = -6.
Negative * Positive = Negative. e.g. (-4) * 3 = -12.
Positive * Negative = Negative. e.g. 3 * (-5) = -15.
4. Dividing rules:
Positive / Positive = Positive. e.g. 14 / 7 = 2.
Negative / Negative = Positive. e.g. (-12) / (-2) = 6.
Negative / Positive = Negative. e.g. (-16) / 8 = -2.
Positive / Negative = Negative. e.g. 12 / (-4) = -3.
Fractions : A mathematical expression denoting the division of two whole numbers is
known as fraction (Cokely and et. al., 2012). Fractions are also used to indicate a
portion of the whole number or a ratio between two numerals. e.g. 5 / 8, 3/ 4, etc. are in
fractional form. Real life example of fraction are listed below:
In our every day life, we use fractions. Fractions are used when sharing of pizza , fruits,
chocolates, etc. are done. Let suppose ravish has only one apple and he has to share this
Operations on positive and negative numbers
There are four operations that are applied on positive and negative numbers that
are listed below:
1. Additive rules:
When two positive numbers are added then the result will also positive (i.e.
positive + positive = positive) . For example : 5 +2 = 7.
When two negative numbers are added then the output will also negative. (i.e.
Negative + Negative = Negative). For example: (-7) + ( -5) = -12
Sum of negative and positive number: Here sign of larger number is taken and
subtraction operation is carried on. Example: (-6) +4 = -10.
2. Subtracting rules :
Negative - positive = Negative. e.g. (-5) - (-4) = -5 + 4 = -9.
Positive - Negative = Positive + Positive = Positive. e.g. 5- (-4) = 5 + 4 = 9.
Negative - Negative = Negative + Positive = Here sign of larger number and
subtraction is performed. e.g. (-6) - (-7) = (-6) + 7 = -1; (-3) - (-6) = (-3) + 6 = 3,
etc.
3. Multiplying rules:
Positive * Positive = Positive. e.g. 4 * 5= 20.
Negative * Negative = Negative. e.g. (-3) * (-2) = -6.
Negative * Positive = Negative. e.g. (-4) * 3 = -12.
Positive * Negative = Negative. e.g. 3 * (-5) = -15.
4. Dividing rules:
Positive / Positive = Positive. e.g. 14 / 7 = 2.
Negative / Negative = Positive. e.g. (-12) / (-2) = 6.
Negative / Positive = Negative. e.g. (-16) / 8 = -2.
Positive / Negative = Negative. e.g. 12 / (-4) = -3.
Fractions : A mathematical expression denoting the division of two whole numbers is
known as fraction (Cokely and et. al., 2012). Fractions are also used to indicate a
portion of the whole number or a ratio between two numerals. e.g. 5 / 8, 3/ 4, etc. are in
fractional form. Real life example of fraction are listed below:
In our every day life, we use fractions. Fractions are used when sharing of pizza , fruits,
chocolates, etc. are done. Let suppose ravish has only one apple and he has to share this
MATI3006- Numeracy1 Summer 2017 Coursework Brief
with his brother. Then he will cut the apple into two equal parts and gives ½ of an apple
to his brother.
Ratios: In mathematics, a ratio denotes a relationship between two numbers reflecting
how many times the first numeral contains the other (Dickert, Kleber and Slovic,
2011). Real life example, if a bowl of vegetables contains five potatoes and seven
onions, then the ratio of potatoes to onions will be 5 : 7.
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online
quiz/activity.
Instruction:
11 Complete your online quiz/activity, (GSM Learn).
11 Take a screenshot.
11 Copy and paste the screenshot here..
Activity 1
Activity 2
with his brother. Then he will cut the apple into two equal parts and gives ½ of an apple
to his brother.
Ratios: In mathematics, a ratio denotes a relationship between two numbers reflecting
how many times the first numeral contains the other (Dickert, Kleber and Slovic,
2011). Real life example, if a bowl of vegetables contains five potatoes and seven
onions, then the ratio of potatoes to onions will be 5 : 7.
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online
quiz/activity.
Instruction:
11 Complete your online quiz/activity, (GSM Learn).
11 Take a screenshot.
11 Copy and paste the screenshot here..
Activity 1
Activity 2
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Activity 3
Activity 3
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
SECTION 2
This section will focus on decimals, percentages and index numbers.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your
answers should show good reflection and awareness of your
strengths and areas for improvement.
I know how to…. I can
do well
I need
practic
e
I’m not
sure
I can’t
do
111 I can describe the relationship
between fractions, decimals and
percentages.
☒ ☐ ☐ ☐
111 I can identify the decimal
equivalent of a percent.
☒ ☐ ☐ ☐
111 I can identify the fractional
equivalent of a percent.
☒ ☐ ☐ ☐
111 I can determine which concepts
and procedures are needed to
complete each practice exercise.
☒ ☐ ☐ ☐
111 I can compute answers by applying
appropriate formulas and
procedures.
☒ ☐ ☐ ☐
111 I can construct a simple index. ☒ ☐ ☐ ☐
111 I can interpret indexes to identify
trends in a data set.
☒ ☐ ☐ ☐
SECTION 2
This section will focus on decimals, percentages and index numbers.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your
answers should show good reflection and awareness of your
strengths and areas for improvement.
I know how to…. I can
do well
I need
practic
e
I’m not
sure
I can’t
do
111 I can describe the relationship
between fractions, decimals and
percentages.
☒ ☐ ☐ ☐
111 I can identify the decimal
equivalent of a percent.
☒ ☐ ☐ ☐
111 I can identify the fractional
equivalent of a percent.
☒ ☐ ☐ ☐
111 I can determine which concepts
and procedures are needed to
complete each practice exercise.
☒ ☐ ☐ ☐
111 I can compute answers by applying
appropriate formulas and
procedures.
☒ ☐ ☐ ☐
111 I can construct a simple index. ☒ ☐ ☐ ☐
111 I can interpret indexes to identify
trends in a data set.
☒ ☐ ☐ ☐
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal
learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also
consider the following points:
Reflect on your learning
How did you contribute in the class?
What went well?
Are there any areas for improvement?
QUESTION 2
Give one example of a ‘real-life’ problem or situation that involves one (or
more) of the following topics:
Decimals
Percentages
Index numbers
Also, please find a solution to the problem you described.
Decimals
A decimal number is a number that consist of a decimal point. A decimal is any
number in the base ten system of mathematics (Garcia-Retamero and Galesic, 2013).
Decimal point is used to isolate the once place from the tenths place in decimals.
Example: 45.37, 57.49, etc.
Percentages
In mathematics, a percentage is a number or ratio stated as a fraction of 100.
Sign of percentage is %. Real life example, if 50 % of the total number of students in
classroom are boy that shows that 50 out of all 100 students are boy.
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal
learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also
consider the following points:
Reflect on your learning
How did you contribute in the class?
What went well?
Are there any areas for improvement?
QUESTION 2
Give one example of a ‘real-life’ problem or situation that involves one (or
more) of the following topics:
Decimals
Percentages
Index numbers
Also, please find a solution to the problem you described.
Decimals
A decimal number is a number that consist of a decimal point. A decimal is any
number in the base ten system of mathematics (Garcia-Retamero and Galesic, 2013).
Decimal point is used to isolate the once place from the tenths place in decimals.
Example: 45.37, 57.49, etc.
Percentages
In mathematics, a percentage is a number or ratio stated as a fraction of 100.
Sign of percentage is %. Real life example, if 50 % of the total number of students in
classroom are boy that shows that 50 out of all 100 students are boy.
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Index number
Index number defines a number by showing how many times the number is used
in a multiplication (Hess and et. al., 2011). It is also known as power. Example: 7 ^2 = 7
* 7 = 49. The smallest digit here is called index number or power.
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online
quiz/activity
Instruction:
11 Complete your online quiz/activity, (GSM Learn).
11 Take a screenshot.
11 Copy and paste the screenshot here.
SECTION 3
This section will focus on introduction to statistics (mean, median, mode and
range) and graphical representation of data.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your
answers should show good reflection and awareness of your
strengths and areas for improvement.
I know how to…. I can
do well
I need
practic
e
I’m not
sure
I can’t
do
111 I know how to calculate a mean. ☒ ☐ ☐ ☐
111 I know how to calculate a median. ☒ ☐ ☐ ☐
111 I know how to calculate a mode. ☒ ☐ ☐ ☐
111 I know how to calculate range. ☒ ☐ ☐ ☐
Index number
Index number defines a number by showing how many times the number is used
in a multiplication (Hess and et. al., 2011). It is also known as power. Example: 7 ^2 = 7
* 7 = 49. The smallest digit here is called index number or power.
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online
quiz/activity
Instruction:
11 Complete your online quiz/activity, (GSM Learn).
11 Take a screenshot.
11 Copy and paste the screenshot here.
SECTION 3
This section will focus on introduction to statistics (mean, median, mode and
range) and graphical representation of data.
Task 1: Skills Audit
Tick the appropriate column for each skill in the list below.
Please note that there is no right or wrong answer. Your
answers should show good reflection and awareness of your
strengths and areas for improvement.
I know how to…. I can
do well
I need
practic
e
I’m not
sure
I can’t
do
111 I know how to calculate a mean. ☒ ☐ ☐ ☐
111 I know how to calculate a median. ☒ ☐ ☐ ☐
111 I know how to calculate a mode. ☒ ☐ ☐ ☐
111 I know how to calculate range. ☒ ☐ ☐ ☐
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
111 I understand the statistical
implications of mean, median,
mode and range.
☒ ☐ ☐ ☐
111 I can define a line graph, bar chart
and a pie chart.
☒ ☐ ☐ ☐
111 I can interpret and analyse graphs
presented to determine what
information is given.
☒ ☐ ☐ ☐
111 I can construct a simple line graph
and bar chart.
☒ ☐ ☐ ☐
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal
learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also
consider the following points:
Reflect on your learning
How did you contribute in the class?
What went well?
Are there any areas for improvement?
QUESTION 2
111 I understand the statistical
implications of mean, median,
mode and range.
☒ ☐ ☐ ☐
111 I can define a line graph, bar chart
and a pie chart.
☒ ☐ ☐ ☐
111 I can interpret and analyse graphs
presented to determine what
information is given.
☒ ☐ ☐ ☐
111 I can construct a simple line graph
and bar chart.
☒ ☐ ☐ ☐
Task 2: In class Activity
QUESTION 1
Reflection
Write a short reflection (approximately 100-150 words) about your personal
learning experience of the topics covered in this section.
You can use the Skills Audit above to facilitate your answer. You may also
consider the following points:
Reflect on your learning
How did you contribute in the class?
What went well?
Are there any areas for improvement?
QUESTION 2
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Give one example of a ‘real-life’ problem or situation that involves one (or
more) of the following topics:
Introduction to statistics (mean, median, mode and range)
Graphical representation of data
Also, please find a solution to the problem you described.
Introduction to statistics
Statistics is a branch of mathematics that deals with grouping, categorization,
analysis and interpretation of numerical facts for drawing reasoning on the basis of their
probability. This explain aggregates of data too large to be apprehensible by average
measurement because such data tends to behave in regular and predictable manner. This
is sub divided into descriptive statistics and inferential statistics.
Mean
Mean can be simply defined as the average of the numbers that is a calculated
central value of a collection of numbers. Mean can be calculated by simply adding all
the numbers and dividing the result by total numbers of digits. For example, mean of
13, 18, 13, 14, 13, 16, 14 , 21 and 13 can be calculated as follow:
Addition of numbers: 13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13 = 135.
Division of result by how many numbers ( that is we added 9 numbers) : 135 / 9 = 15.
so, the mean is 15.
Median
Median is nothing but the middle value or number present in a sorted list of
numbers (Kahan and et. al., 2012). To calculate median of {13, 23, 11, 16, 15, 10, 26}
following steps are followed:
Step 1: putting them in ascending order that is {10, 11, 13, 15, 16, 23, 26}.
Step 2: The middle number is 15, so the median here is 15.
Note: if there are two middle numbers , then average is calculated.
Mode
The mode can be simply defined as the number that are appears most often in a
set or collection of numbers. For example : in { 6, 3, 5, 6, 6, 6, 9, 3, 9}. Here the mode
will be 6 as it appears most the time here (i.e. 4 times).
Give one example of a ‘real-life’ problem or situation that involves one (or
more) of the following topics:
Introduction to statistics (mean, median, mode and range)
Graphical representation of data
Also, please find a solution to the problem you described.
Introduction to statistics
Statistics is a branch of mathematics that deals with grouping, categorization,
analysis and interpretation of numerical facts for drawing reasoning on the basis of their
probability. This explain aggregates of data too large to be apprehensible by average
measurement because such data tends to behave in regular and predictable manner. This
is sub divided into descriptive statistics and inferential statistics.
Mean
Mean can be simply defined as the average of the numbers that is a calculated
central value of a collection of numbers. Mean can be calculated by simply adding all
the numbers and dividing the result by total numbers of digits. For example, mean of
13, 18, 13, 14, 13, 16, 14 , 21 and 13 can be calculated as follow:
Addition of numbers: 13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13 = 135.
Division of result by how many numbers ( that is we added 9 numbers) : 135 / 9 = 15.
so, the mean is 15.
Median
Median is nothing but the middle value or number present in a sorted list of
numbers (Kahan and et. al., 2012). To calculate median of {13, 23, 11, 16, 15, 10, 26}
following steps are followed:
Step 1: putting them in ascending order that is {10, 11, 13, 15, 16, 23, 26}.
Step 2: The middle number is 15, so the median here is 15.
Note: if there are two middle numbers , then average is calculated.
Mode
The mode can be simply defined as the number that are appears most often in a
set or collection of numbers. For example : in { 6, 3, 5, 6, 6, 6, 9, 3, 9}. Here the mode
will be 6 as it appears most the time here (i.e. 4 times).
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Range
Range can be defined as the difference between smallest and largest numbers
present in a set of numbers. For example: In { 5, 6, 4, 3, 2, 9} , the smallest number is 2
and the largest one is 9. So, the range will be 9 – 2 = 7.
Graphical representation of data
Graphical representation is another method of analysing numerical value. A
graph is a sort of chart via which statistical data are presentation are done that is in the
form of lines or curves. This is drawn across the interconnected or coordinated points
plotted on its surface. Graphs are enabling students in learning the cause and are
effecting the relationship between two variables (Steele and et. al., 2012). Graph
assists in measuring the extent of alteration or change in one variable when the other
variable changes by a specific amount. It also aids in enabling the study of both time
series and distribution of frequency as this provide clear account and precision image of
problems. They are very easier to understand and are eye catching. There are commonly
four types of graph that are line graphs, bar graphs and histograms. Pie charts, and
Cartesian graphs.
Real life example of graph has been given below:
Here the number of number of workers and their age in years are explained in a graph.
Range
Range can be defined as the difference between smallest and largest numbers
present in a set of numbers. For example: In { 5, 6, 4, 3, 2, 9} , the smallest number is 2
and the largest one is 9. So, the range will be 9 – 2 = 7.
Graphical representation of data
Graphical representation is another method of analysing numerical value. A
graph is a sort of chart via which statistical data are presentation are done that is in the
form of lines or curves. This is drawn across the interconnected or coordinated points
plotted on its surface. Graphs are enabling students in learning the cause and are
effecting the relationship between two variables (Steele and et. al., 2012). Graph
assists in measuring the extent of alteration or change in one variable when the other
variable changes by a specific amount. It also aids in enabling the study of both time
series and distribution of frequency as this provide clear account and precision image of
problems. They are very easier to understand and are eye catching. There are commonly
four types of graph that are line graphs, bar graphs and histograms. Pie charts, and
Cartesian graphs.
Real life example of graph has been given below:
Here the number of number of workers and their age in years are explained in a graph.
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online
quiz/activity.
Instruction:
11 Complete your online quiz/activity, (GSM Learn).
11 Take a screenshot.
11 Copy and paste the screenshot here. .
Task 3: Online Activity
Evidence (screenshot) of completing and passing relevant online
quiz/activity.
Instruction:
11 Complete your online quiz/activity, (GSM Learn).
11 Take a screenshot.
11 Copy and paste the screenshot here. .
MATI3006- Numeracy1 Summer 2017 Coursework Brief
SECTION 4
QUESTION. 1 [6 marks]
In 2011, 350,800 individuals were awarded a first degree, compared
to 243,246 in 2000 in England and Wales. What was the percentage
change over this decade.
Answer (type your answer and calculations here):
Percentage change occurred = 350,800 – 243,246 = 107554
107554 / 350,800 = 0.306596351 * 100 = 30.65963512 or 30.65 %.
[Mathematical rule of percentage: actual amount / total amount * 100
]
QUESTION. 2 [6
marks]
The number of females that achieved a first degree in 1980 was
25,319, in the UK. Over the next ten years this number increased by
33.76%. How many females achieved a first degree in 1990?
Answer (type your answer and calculations here):
Females achieved first degree in 1900 = 33.76 / 100 * 25319 =
8547.7+ 25,319.0 = 33866.7
QUESTION.3 [5
marks]
In 2000 there were 986,267 students admitted to university in
England and Wales. This is 4.7% more than in year 1999. How many
students were admitted in 1999?
Answer (type your answer and calculations here):
Students admitted in 1999= 4.7 /100 * 986267 = 46354.549 +
986,267= 1032621.549
SECTION 4
QUESTION. 1 [6 marks]
In 2011, 350,800 individuals were awarded a first degree, compared
to 243,246 in 2000 in England and Wales. What was the percentage
change over this decade.
Answer (type your answer and calculations here):
Percentage change occurred = 350,800 – 243,246 = 107554
107554 / 350,800 = 0.306596351 * 100 = 30.65963512 or 30.65 %.
[Mathematical rule of percentage: actual amount / total amount * 100
]
QUESTION. 2 [6
marks]
The number of females that achieved a first degree in 1980 was
25,319, in the UK. Over the next ten years this number increased by
33.76%. How many females achieved a first degree in 1990?
Answer (type your answer and calculations here):
Females achieved first degree in 1900 = 33.76 / 100 * 25319 =
8547.7+ 25,319.0 = 33866.7
QUESTION.3 [5
marks]
In 2000 there were 986,267 students admitted to university in
England and Wales. This is 4.7% more than in year 1999. How many
students were admitted in 1999?
Answer (type your answer and calculations here):
Students admitted in 1999= 4.7 /100 * 986267 = 46354.549 +
986,267= 1032621.549
MATI3006- Numeracy1 Summer 2017 Coursework Brief
QUESTION.4 [5
marks]
In 2014, 734,037 students were admitted to specialist programmes of
study across universities in England and Wales. The data gathered
was then used to construct the pie chart:
Using the pie chart above, please answer the following questions:
a) Which subject area has the second highest number of students?
b) Which subject area admitted the lowest number of students?
c) What percentage of the students are reading Law?
d) How many students are undertaking Business & Administrative
studies?
e) How many more students are doing computer science than
biological science?
Answer (type your answer and calculations here):
QUESTION 5 [6 marks]
QUESTION.4 [5
marks]
In 2014, 734,037 students were admitted to specialist programmes of
study across universities in England and Wales. The data gathered
was then used to construct the pie chart:
Using the pie chart above, please answer the following questions:
a) Which subject area has the second highest number of students?
b) Which subject area admitted the lowest number of students?
c) What percentage of the students are reading Law?
d) How many students are undertaking Business & Administrative
studies?
e) How many more students are doing computer science than
biological science?
Answer (type your answer and calculations here):
QUESTION 5 [6 marks]
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
Using the data presented in the bar chart above, answer the following
questions:
1a What percentages of people living in England are working part-time?
Answer a: 19 %
1b What percentage of students living in Royal Greenwich, are in
employment full-time?
Answer b: 55 %1c How many more (percentage) people are in full-time employment
than are self-employed in London?
Answer c:: 40 %
Using the data presented in the bar chart above, answer the following
questions:
1a What percentages of people living in England are working part-time?
Answer a: 19 %
1b What percentage of students living in Royal Greenwich, are in
employment full-time?
Answer b: 55 %1c How many more (percentage) people are in full-time employment
than are self-employed in London?
Answer c:: 40 %
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Please answer questions 6-8 using the information below:
First year students by level and mode of study 2005/06 to 2015/16
Year Postgraduat
e part-time
Postgraduate
full-time
Undergraduat
e part-time
Undergraduat
e full-time Total
2015/
16 107,120 210,945 148,570 525,490 992,125
2014/
15 107,950 209,805 157,835 513,295 988,890
2013/
14 106,260 211,875 175,375 502,230 995,740
2012/
13 102,890 203,155 199,940 466,270 972,255
2011/
12 109,535 207,665 278,530 521,605 1,117,335
2010/
11 127,750 207,595 301,025 509,065 1,145,435
2009/
10 132,790 200,880 334,820 516,770 1,185,260
2008/
09 129,055 177,595 344,775 493,425 1,144,850
2007/
08 116,570 161,015 332,320 458,575 1,068,475
2006/
07 116,220 162,575 341,035 437,775 1,057,610
2005/
06 114,940 155,665 337,240 450,485 1,058,330
QUESTION. 6 [4
marks]
In 2011/12, what percentages of students were undertaking part-time
postgraduate study?
Answer (type your answer and calculations here):
9.8 %
QUESTION.7 [4
marks]
In 2015/16 what was the ratio of postgraduate part-time students to
undergraduate full-time students?
Please answer questions 6-8 using the information below:
First year students by level and mode of study 2005/06 to 2015/16
Year Postgraduat
e part-time
Postgraduate
full-time
Undergraduat
e part-time
Undergraduat
e full-time Total
2015/
16 107,120 210,945 148,570 525,490 992,125
2014/
15 107,950 209,805 157,835 513,295 988,890
2013/
14 106,260 211,875 175,375 502,230 995,740
2012/
13 102,890 203,155 199,940 466,270 972,255
2011/
12 109,535 207,665 278,530 521,605 1,117,335
2010/
11 127,750 207,595 301,025 509,065 1,145,435
2009/
10 132,790 200,880 334,820 516,770 1,185,260
2008/
09 129,055 177,595 344,775 493,425 1,144,850
2007/
08 116,570 161,015 332,320 458,575 1,068,475
2006/
07 116,220 162,575 341,035 437,775 1,057,610
2005/
06 114,940 155,665 337,240 450,485 1,058,330
QUESTION. 6 [4
marks]
In 2011/12, what percentages of students were undertaking part-time
postgraduate study?
Answer (type your answer and calculations here):
9.8 %
QUESTION.7 [4
marks]
In 2015/16 what was the ratio of postgraduate part-time students to
undergraduate full-time students?
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Answer (type your answer and calculations here):
1:5
QUESTION.8 [5 marks]
Taking into account data for the years 2005/06 to 2010/11 of part-
time undergraduate students, please calculate the following:
a) Mean
b) Median
c) Range
Answer (type your answer and calculations here):
Mean = (337240 + 341035+ 332320+344775+334820) / 5=338038.
Median = 33720; 341035 ; 332320; 344775; 334820
= (341035+332320)/2 = 336677.5
Mode = 344775 (Largest number)
Please answer questions 9-10 using the information below:
Answer (type your answer and calculations here):
1:5
QUESTION.8 [5 marks]
Taking into account data for the years 2005/06 to 2010/11 of part-
time undergraduate students, please calculate the following:
a) Mean
b) Median
c) Range
Answer (type your answer and calculations here):
Mean = (337240 + 341035+ 332320+344775+334820) / 5=338038.
Median = 33720; 341035 ; 332320; 344775; 334820
= (341035+332320)/2 = 336677.5
Mode = 344775 (Largest number)
Please answer questions 9-10 using the information below:
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MATI3006- Numeracy1 Summer 2017 Coursework Brief
Median hourly earnings: Age by qualification and sex, 2000 to 2010,
UK
Source: Labour Force Survey - Office for National Statistics
Degree N
o
D
e
g
r
e
e
Men Women Men Women
Age 22 £9.10 £8.80 £8.10 £7.40
23 £10.20 £9.80 £8.60 £7.80
24 £11.40 £10.80 £9.00 £8.10
25 £12.50 £11.60 £9.50 £8.40
26 £13.50 £12.50 £9.70 £8.70
27 £14.50 £13.20 £10.10 £9.10
28 £15.50 £14.00 £10.70 £9.30
29 £16.70 £14.80 £11.10 £9.40
30 £17.70 £15.50 £11.50 £9.70
31 £18.40 £15.60 £11.70 £9.90
32 £18.90 £16.20 £12.00 £9.70
33 £19.50 £16.60 £12.20 £9.80
34 £20.40 £16.50 £12.70 £9.80
35 £21.00 £17.00 £12.60 £10.10
36 £20.80 £16.80 £12.90 £9.90
37 £21.20 £16.90 £12.90 £9.80
38 £21.60 £17.00 £13.00 £9.60
39 £22.30 £16.80 £13.10 £9.70
40 £22.00 £16.90 £13.10 £9.60
41 £22.10 £16.60 £13.10 £9.60
42 £22.30 £16.30 £13.20 £9.50
43 £22.50 £16.50 £13.20 £9.60
44 £22.30 £16.70 £13.50 £9.40
45 £22.60 £16.50 £13.40 £9.40
46 £22.70 £16.70 £13.20 £9.20
47 £22.20 £16.60 £13.20 £9.30
48 £22.30 £16.70 £13.30 £9.30
49 £22.50 £16.80 £13.20 £9.20
50 £22.10 £16.90 £13.00 £9.40
51 £22.80 £17.00 £13.00 £9.20
52 £22.20 £16.60 £12.80 £9.10
53 £22.20 £16.80 £12.50 £9.00
54 £21.90 £16.80 £12.50 £9.00
55 £21.30 £16.90 £12.50 £8.90
56 £21.40 £16.80 £12.10 £8.70
57 £20.60 £16.40 £11.90 £8.80
58 £20.20 £16.50 £11.60 £8.80
59 £20.50 £15.70 £11.70 £8.70
60 £19.70 £16.00 £11.50 £8.90
61 £19.20 £15.40 £10.80 £8.70
62 £19.20 £15.60 £10.50 £8.50
Median hourly earnings: Age by qualification and sex, 2000 to 2010,
UK
Source: Labour Force Survey - Office for National Statistics
Degree N
o
D
e
g
r
e
e
Men Women Men Women
Age 22 £9.10 £8.80 £8.10 £7.40
23 £10.20 £9.80 £8.60 £7.80
24 £11.40 £10.80 £9.00 £8.10
25 £12.50 £11.60 £9.50 £8.40
26 £13.50 £12.50 £9.70 £8.70
27 £14.50 £13.20 £10.10 £9.10
28 £15.50 £14.00 £10.70 £9.30
29 £16.70 £14.80 £11.10 £9.40
30 £17.70 £15.50 £11.50 £9.70
31 £18.40 £15.60 £11.70 £9.90
32 £18.90 £16.20 £12.00 £9.70
33 £19.50 £16.60 £12.20 £9.80
34 £20.40 £16.50 £12.70 £9.80
35 £21.00 £17.00 £12.60 £10.10
36 £20.80 £16.80 £12.90 £9.90
37 £21.20 £16.90 £12.90 £9.80
38 £21.60 £17.00 £13.00 £9.60
39 £22.30 £16.80 £13.10 £9.70
40 £22.00 £16.90 £13.10 £9.60
41 £22.10 £16.60 £13.10 £9.60
42 £22.30 £16.30 £13.20 £9.50
43 £22.50 £16.50 £13.20 £9.60
44 £22.30 £16.70 £13.50 £9.40
45 £22.60 £16.50 £13.40 £9.40
46 £22.70 £16.70 £13.20 £9.20
47 £22.20 £16.60 £13.20 £9.30
48 £22.30 £16.70 £13.30 £9.30
49 £22.50 £16.80 £13.20 £9.20
50 £22.10 £16.90 £13.00 £9.40
51 £22.80 £17.00 £13.00 £9.20
52 £22.20 £16.60 £12.80 £9.10
53 £22.20 £16.80 £12.50 £9.00
54 £21.90 £16.80 £12.50 £9.00
55 £21.30 £16.90 £12.50 £8.90
56 £21.40 £16.80 £12.10 £8.70
57 £20.60 £16.40 £11.90 £8.80
58 £20.20 £16.50 £11.60 £8.80
59 £20.50 £15.70 £11.70 £8.70
60 £19.70 £16.00 £11.50 £8.90
61 £19.20 £15.40 £10.80 £8.70
62 £19.20 £15.60 £10.50 £8.50
MATI3006- Numeracy1 Summer 2017 Coursework Brief
63 £19.70 £15.40 £10.40 £8.60
64 £19.20 £15.60 £10.40 £8.60
QUESTION.9 [4 marks]
What is the percentage difference in earnings between a 34 year old
female with and without a degree?
Answer (type your answer and calculations here):
QUESTION.10 [10
marks]
Using the data above of the hourly earnings of individuals based on
Age, Qualification and Sex from 2000 to 2010, calculate for all four
categories the following:
a) Mean
b) Median
c) Mode
c) Range
Answer (type your answer and calculations here):
a) Mean = 840.9
b) Median= 44
c) Mode= 19.2 (3 times repeated )
The End
63 £19.70 £15.40 £10.40 £8.60
64 £19.20 £15.60 £10.40 £8.60
QUESTION.9 [4 marks]
What is the percentage difference in earnings between a 34 year old
female with and without a degree?
Answer (type your answer and calculations here):
QUESTION.10 [10
marks]
Using the data above of the hourly earnings of individuals based on
Age, Qualification and Sex from 2000 to 2010, calculate for all four
categories the following:
a) Mean
b) Median
c) Mode
c) Range
Answer (type your answer and calculations here):
a) Mean = 840.9
b) Median= 44
c) Mode= 19.2 (3 times repeated )
The End
MATI3006- Numeracy1 Summer 2017 Coursework Brief
Marking Criteria
Generic Criteria for Assessment at Level 3
Assessment
categories
Knowledge &
Understanding
of Subject
Inadequate
understanding of
and major gaps
in knowledge.
Significant
inaccuracies.
Limited
understanding of
and large gaps in
knowledge
evident.
Some
inaccuracies.
Threshold level.
Basic and broadly
accurate knowledge
and understanding
of the material.
Some elements
missing and flaws
evident.
Satisfactory,
routine knowledge
and understanding
of
the material, main
concepts
Some flaws may
be evident.
Good,
consistent
knowledge and
understanding
of the
material, main
concepts at
this level.
Excellent
knowledge and
understanding
of the main
concepts at
this level.
Excepti
onal
knowle
dge
and
unders
tandin
g of
Material and
concepts at
this level.Cognitive/
Intellectual
Skills
(e.g. analysis
and synthesis;
logic and
argument;
analytical
reflection;
organisation and
communication
of ideas and
evidence)
Inadequate
views based on
personal opinion.
Complete lack of
supporting
evidence.
Inadequate or
complete lack of
conclusions.
Limited logic and
analysis, and
lack of consistent
argument. Points
generally
descriptive and
at times
incoherent.
Conclusions lack
validity.
Threshold level.
Basic awareness
of issues. Some
logical arguments
evident. Lacks
coherence in places.
Some inconsistency
in evidence to
support views. Some
broadly valid
conclusions
included.
Issues identified
satisfactorily
within given areas.
Demonstration of
the ability to use
evidence to
support a coherent
argument.
Some generally
valid conclusions
included.
Good
analytical
ability.
Arguments
generally
logical, largely
balanced,
coherently
expressed and
supported with
evidence.
Sound
conclusions
included.
Excellent
logical analysis
throughout.
Persuasive
points made
within given
areas of the
work..
Arguments
well-
balanced and
logically
developed and
supported with
a range of
Exceptiona
lly logical
analysis
throughout
.
Persuasive
argument
s included
throughou
t the
work
supported
by
appropriat
ely
Use of
Research-
informed
Literature
(including
referencing,
appropriate
academic
conventions and
academic
honesty)
Inadequate
evidence of any
background
reading. Views
are inadequately
supported.
Inadequate / no
use of academic
conventions at
this level.
Evidence of
limited reading
around the topic
of the work.
Sources
inaccurately
utilised.
Limited use of
academic
conventions at
this level.
Threshold level.
Some evidence of
reading around the
topic of the work.
Basic academic
conventions
followed at this
level, but with
errors.
Satisfactory range
of literature used
mainly
descriptively.
Academic skills
generally sound at
this level.
Good range of
relevant
literature
generally used
critically to
inform
argument.
Good use of
academic
conventions at
this level.
Excellent
range of
relevant
literature used
critically to
inform
argument.
Consistently
accurate use of
academic
conventions at
this level.
Exceptio
nal
range of
relevant
literature
used
critically to
inform
argument.
Consistently
accurate
and skilful
use of
academic
conventions
at this level.
Marking Criteria
Generic Criteria for Assessment at Level 3
Assessment
categories
Knowledge &
Understanding
of Subject
Inadequate
understanding of
and major gaps
in knowledge.
Significant
inaccuracies.
Limited
understanding of
and large gaps in
knowledge
evident.
Some
inaccuracies.
Threshold level.
Basic and broadly
accurate knowledge
and understanding
of the material.
Some elements
missing and flaws
evident.
Satisfactory,
routine knowledge
and understanding
of
the material, main
concepts
Some flaws may
be evident.
Good,
consistent
knowledge and
understanding
of the
material, main
concepts at
this level.
Excellent
knowledge and
understanding
of the main
concepts at
this level.
Excepti
onal
knowle
dge
and
unders
tandin
g of
Material and
concepts at
this level.Cognitive/
Intellectual
Skills
(e.g. analysis
and synthesis;
logic and
argument;
analytical
reflection;
organisation and
communication
of ideas and
evidence)
Inadequate
views based on
personal opinion.
Complete lack of
supporting
evidence.
Inadequate or
complete lack of
conclusions.
Limited logic and
analysis, and
lack of consistent
argument. Points
generally
descriptive and
at times
incoherent.
Conclusions lack
validity.
Threshold level.
Basic awareness
of issues. Some
logical arguments
evident. Lacks
coherence in places.
Some inconsistency
in evidence to
support views. Some
broadly valid
conclusions
included.
Issues identified
satisfactorily
within given areas.
Demonstration of
the ability to use
evidence to
support a coherent
argument.
Some generally
valid conclusions
included.
Good
analytical
ability.
Arguments
generally
logical, largely
balanced,
coherently
expressed and
supported with
evidence.
Sound
conclusions
included.
Excellent
logical analysis
throughout.
Persuasive
points made
within given
areas of the
work..
Arguments
well-
balanced and
logically
developed and
supported with
a range of
Exceptiona
lly logical
analysis
throughout
.
Persuasive
argument
s included
throughou
t the
work
supported
by
appropriat
ely
Use of
Research-
informed
Literature
(including
referencing,
appropriate
academic
conventions and
academic
honesty)
Inadequate
evidence of any
background
reading. Views
are inadequately
supported.
Inadequate / no
use of academic
conventions at
this level.
Evidence of
limited reading
around the topic
of the work.
Sources
inaccurately
utilised.
Limited use of
academic
conventions at
this level.
Threshold level.
Some evidence of
reading around the
topic of the work.
Basic academic
conventions
followed at this
level, but with
errors.
Satisfactory range
of literature used
mainly
descriptively.
Academic skills
generally sound at
this level.
Good range of
relevant
literature
generally used
critically to
inform
argument.
Good use of
academic
conventions at
this level.
Excellent
range of
relevant
literature used
critically to
inform
argument.
Consistently
accurate use of
academic
conventions at
this level.
Exceptio
nal
range of
relevant
literature
used
critically to
inform
argument.
Consistently
accurate
and skilful
use of
academic
conventions
at this level.
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