FASTP 1013: Mathematics and Introductory Statistics Assessment

Assessment 

Probability and Statistics

This assignment is designed to assess your ability to calculate probability in real life situations and to interpret statistics and create graphs that give useful information about data.

If you do not have access to a computer, you can make a booking and do it in a computer lab in your campus.

Section 1: Interpreting the results of a survey

A survey was conducted to find out how a group of university students use their mobile phones. The survey included a number of participants and gathered a range of data about age, gender, brand, model, service provider, phone costs, etc.

Using the data provided, analyse and interpret the results by answering the following series of questions. Make sure that any written answers are clear, and that you answer each question as full as possible.

Questions

1. Phone plans and networks

a) Create a two-way table that shows the mobile plan type (Prepaid or Plan) and the type of network they are on.

b) Create a stacked bar graph or side by side bar graph that compares a person’s mobile phone plan type (Prepaid or Plan) with the network they are on.

c) Using the information in Question 2a and 2b, describe the differences between mobile users on each of the different networks, if there are any differences. For example, are Telstra users more likely to be on a Plan or Prepaid? What percentage of respondents use Telstra?, etc.

2. Connecting to the internet

• Create a pie chart that indicates the way that respondents most frequently connect with the internet. What percentage of users use Wifi? 4G/5G? Is this what you would expect?

Brief Summary of Assessment Requirements

This Probability and Statistics assignment assesses a student’s ability to apply statistical tools to real-world data and interpret results meaningfully. The assessment focuses on analysing survey data collected from university students about their mobile phone usage. Students are required to:

Key Components of the Assessment

1. Section 1 Interpreting Survey Data

   • Two-way table:
     Create a table comparing mobile phone plan type (Prepaid vs. Plan) with network providers.
   • Bar Graph:
     Present this comparison visually using either a stacked bar graph or a side-by-side bar graph.
   • Data Interpretation:
     Describe patterns, differences, or trends across networks (e.g., which network has more Plan users, percentage of Telstra users, etc.).

2. Section 2 Connecting to the Internet

   • Pie Chart:
     Display how respondents most frequently connect to the internet (Wi-Fi, 4G/5G).
   • Interpretation:
     Identify percentages for each connection type and evaluate whether the results align with general expectations.

Key Pointers to Cover in the Assessment

• Accurate data representation through tables and graphs
• Correct use of statistical terminology
• Clear interpretation of patterns and percentages
• Logical explanation of findings
• Ability to connect numerical data to real-life usage behaviours

How the Academic Mentor Guided the Student Step-by-Step Approach

The academic mentor followed a structured process to ensure the student understood both the statistical methods and the purpose behind each task.

Step 1: Understanding the Assessment Purpose

The mentor first explained that the assignment aims to test:

• Ability to work with real survey data
• Skills in creating statistical representations
• Competence in analysing numerical information to draw meaningful conclusions

This foundation helped the student understand why each section is important.

Step 2: Reviewing the Survey Data

The mentor guided the student through the dataset, helping them:

• Identify relevant variables (plan type, network provider, internet connection type)
• Group data into categories required for tables and graphs
• Check the accuracy of inputs before building visuals

Step 3: Creating the Two-Way Table

The mentor explained:

• How to organise frequencies of Plan vs. Prepaid users across all network types
• How to ensure totals are correct
• How the table becomes the base for later interpretations

The student learned how to convert raw data into a structured format.

Step 4: Developing the Bar Graph

The mentor demonstrated:

• How to choose between stacked or side-by-side bar graphs
• How to label axes clearly
• Why visual comparison helps identify trends faster
• How bar heights represent proportions or counts

The student was shown how to visually communicate data effectively.

Step 5: Interpreting the Plan vs. Network Results

The mentor guided the student on:

• Identifying which networks have more Plan or Prepaid users
• Calculating relevant percentages
• Linking patterns to possible real-world explanations (e.g., Telstra’s pricing, student preferences, etc.)

This strengthened the student’s analytical reasoning.

Step 6: Creating the Pie Chart for Internet Usage

The mentor helped by:

• Calculating frequency and percentage for each connection method
• Choosing appropriate labels and segments
• Ensuring proportions add up to 100%

The student learned correct visualisation techniques for categorical data.

Step 7: Analysing the Internet Connection Results

The mentor explained how to:

• Comment on the dominant connection type
• Compare Wi-Fi vs. mobile data usage
• Evaluate whether the findings align with general patterns among students

This reinforced interpretation skills and critical thinking.

Final Outcome and Learning Objectives Achieved

Outcome Achieved

The student produced:

• A complete two-way table
• Correctly formatted bar and pie charts
• Well-explained interpretations based on statistical evidence
• Clear, accurate conclusions drawn from the survey findings

The final work demonstrated both technical accuracy and strong analytical writing.

Learning Objectives Covered

By completing the assessment under mentor guidance, the student met the following objectives:

• Statistical Skills:
  Constructing tables, bar graphs, and pie charts accurately.
• Data Interpretation:
  Understanding what the numbers reveal about user behaviour.
• Critical Thinking:
  Explaining real-life implications of the statistical results.
• Communication:
  Writing clear and meaningful explanations based on evidence.
• Application of Probability & Statistics in Real Contexts:
  Using survey data to understand everyday phenomena like phone usage.

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