Instructions:

Prepare a report using an appropriate word processing package e.g. Microsoft Word, to explain

your investigations into the tasks specified in this assessment. Please include appropriate

images and results of the work done (calculations and Excel/Geogebra) to support your reported

findings. Your completed work should be uploaded to study smart in a single word-processed

report.

The maximum mark for this assessment is 56 and will comprise 25% of your overall mark for the

module.

Learning outcomes assessed:

Knowledge and Understanding

KU2:  Evaluate  the  strengths  and  weaknesses  of  alternative  models,  and  consequently,  of  any

conclusions drawn.

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a problem.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

Evidence for Assessment:

Report written using an appropriate software.

Submission Details:

On completion, your report should be uploaded, using only your Student ID, to the Assessment Tab on Study Smart. You must not use your name on the submission, either within the document or as the file name when uploading to TurnItIn.

All submissions will be processed utilising TurnitIn and compared with documents on the Internet.

Your report needs to be original. If it is believed from the TurnitIn report or otherwise, that your assignment is too similar to another work, you will be asked to explain your report during a live viva.Academic Impropriety:

You are reminded that plagiarism is the unreferenced use of other people’s work or your own previous work. This could include visual images, sound recordings, diagrams, as well as written text. You can however use other people’s work as examples, supporting evidence or inspiration as long as it is referenced appropriately.

Academic Impropriety also includes copying or using other people’s work and presenting this as your own. This could include work produced by family members, friends or unknown people on the Internet.

If you are guilty of Academic Impropriety you are likely to have your grade for the assignment reduced to zero.

Task 1 – Performance in STEM Subjects 16 Marks

Two different teachers in a school use different methods to teach two groups of students. Both groups of students sat the same examination at the end of the course. The students’ marks are shown in the groups frequency table and are recorded as percentages:

Performance (%)

Group A

Group B

In addition,

•   The highest score for both groups was 88%

•   The lowest score 22% for group A and 21% for group B.

Write a short report comparing the data for both groups

-     Calculate appropriate measures of location and dispersion

-     Discuss the advantages and disadvantages of each measure, with reference to your data

-     Compare both groups and explain whether or not you believe that one method of teaching is better than the other.

You must include appropriate diagrams to illustrate your report explaining how the choice of the diagrams facilitates comparison between the performances in both schools. You need to use    diagrams to compare both schools.

Learning Outcomes Assessed

Knowledge and Understanding

KU2: Evaluate the strengths and weaknesses of alternative models, and consequently, of any conclusions

drawn.

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as appropriate.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

Task 2 – Increase in Property Purchase Loans 12 Marks

The CEO of a company would like to review the opening hours of the department store run by his company. His business analyst has found the number of visits to the store during the last  four years in four different time slots.

Year                                     2018                                                 2019                                                 2020                                                 2021

Time Slot      T1         T2          T3         T4          T1          T2          T3         T4          T1         T2          T3         T4          T1         T2         T3         T4

No of             1200      1412      1810      1900      1320      1520      2102      2200      1530      1670      2310      2300      1600      1800      2200      2350

Customers

You need to write a report analysing the trend on the number of new purchases over these 4 years.

Your report should include:

•   A time series graph, with 4 point moving averages and trend line.

•   A description in your own words of the observed trend in the given data within the given period of time.

•   An explanation of what the trend line represents and what is the difference between the values given by the trend line and the observed values.

•   A prediction for the number of customers of the company in 2022.

You need to explain if the prediction made is reliable and what factors could influence this prediction.

Learning Outcomes Assessed

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a problem.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

Task 3 – Statistical Distribution 12 Marks

It was well known that for a phone manufacturer, 2% of phones made is defective.

Different samples of phones are to be tested, and in each sample any bags with imperfections are rejected before sale.

You are to write a report to assess the chances of finding defective phones in the given              samples. Note that the company wants to reduce the number of defective phones to a particular level.

In your report you must state:

•   A suitable distribution to model the number of defective phones and an explanation of why using such a distribution

•   All the assumptions needed to model this situation with the chosen distribution and a comment on their validity

•   Calculations of all the appropriate probabilities considering three different samples,     with appropriate comment on the values of the probabilities and the number of phones chosen in the samples.

You need to show all working using appropriate spreadsheets (e.g., Excel) and you need to provide full explanations in your own words.

Learning Outcomes Assessed

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as appropriate.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

Grade Rubric – Business Mathematics

Coursework (Statistics and Probability)

Task 1 – Performance in Maths 16 Marks

0 Marks: Insufficient display of understanding and knowledge

I. Measures of Location and Dispersion

1 Mark: One correct measure found with no calculations

2 Marks: Two correct measures calculated with correct calculations shown

3 Marks: All correct measures of location or dispersion calculated with correct calculations      shown OR at least two measures of location and one measure of dispersion found with correct calculations.

4 Marks: All measures of location AND dispersion correctly found with correct calculation.

II. Advantages and Disadvantages

1 Mark: Attempt at finding an advantage OR Disadvantage of one measure

2 Marks: Advantage and disadvantage stated for at least two measures

3 Marks: Advantages and disadvantages stated for more than two measures (at least one measure of location and one measure of dispersion)

4 Marks: Advantages and disadvantages stated for all measures.

III. Diagram(s)

1 Mark: attempt at drawing an appropriate diagram

2 Marks: At least one correct diagram shown with no explanation

3 Marks: At least one correct diagram shown with some explanation

4 Marks: Correct diagrams shown with clear explanation and explanation of why are appropriate

IV. Comparison

1 Mark: Attempt at giving a comparison between both groups

2 Marks: Basic comparison with no or poor explanation

3 Marks: Good comparison with little explanation

4 Marks: Good comparison with clear explanation and address if one method is better than the other

Learning Outcomes Assessed

Knowledge and Understanding

KU2: Evaluate the strengths and weaknesses of alternative models, and consequently, of any conclusions

drawn.

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a problem .

Task 2 – Rice Production

0 Marks: Not enough work to achieve marks

I. Diagram(s)

1 Mark: Attempt at producing a diagram

2 Marks: Correct time series graph with no moving averages nor trend line

3 Marks: Correct time series graph with correct moving averages OR correct trend line

4 Marks: Correct time series graph with correct moving averages AND correct trend line II.

II. Description

1 Mark: Attempt at describing the trend

2 Marks: Basic explanation of the trend with no mention to the trend line

3 Marks: Good explanation of the trend with mention to the trend line

4 Marks: Good explanation of the trend and good description of what trend line represents II

III. Comparison and prediction

1 Mark: Attempt at comparison or prediction

2 Marks: Little explanation of difference between observed values and trend line and no prediction given

3 Marks: Good explanation of difference between observed values and trend line with attempt at prediction. Little explanation on reliability.

4 Marks: Good explanation of difference between observed values and trend line with correct prediction. Clear explanation on reliability with external factors included.

Learning Outcomes Assessed

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a problem .

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

Task 3 – Statistical Distributions

0 Marks: Not enough work to achieve marks

I. Modelling

1 Mark: Attempt at stating a model for the problem

2 Marks: Correct distribution, poor notation and no or poor explanation

3 Marks: Correct distribution with correct notation and little explanation

4 Marks: Correct distribution with correct notation and good explanation

II. Assumptions

1 Mark: Attempt at stating any assumption

2 Marks: At least one correct assumption with no comments on validity

3 Marks: At least two correct assumptions with basic comment on validity

4 Marks: At least three correct assumptions with good comments on validity

III. Calculations

1 Mark: Attempt at finding at least one probability

2 Marks: Only one sample considered with some calculations and no explanation given

3 Marks: At least two samples considered with calculations and little explanation given

4 Marks: At least three samples considered with calculations and good explanation given

Learning Outcomes Assessed

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as appropriate.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.