K17MA Statistics Assignment: Real-World Case Study on NBA, Probability & Data Analysis
| University | UCSI University (UCSI) |
| Subject | K17MA Advanced Mathematics For Science |
APPLICATIONS OF STATISTICAL ANALYSIS IN REAL-WORLD PROBLEMS
Statistical analysis is a fundamental tool for understanding and solving real-world problems. Through various techniques such as experimental design, graphical representation of data, probability calculations, and inferential statistics, we can make informed decisions, predict outcomes, and assess risks in diverse fields. By applying statistical methods, we can validate
claims, analyse trends, and estimate parameters that describe complex systems, from scientific studies to business and sports analytics.
TASK 1: Experimental Design and Inference (5 marks)
A nutrition research company conducted a study with 25 volunteers to test the effects of a new supplement called “NutriCore” over 3 months. The company reported an improvement in energy levels based on participants’ self-assessment.
Question:
Why can’t we conclude from this study that “NutriCore” increases energy levels for the entire population?
Provide at least two strong statistical reasons related to sample size, bias, or study design.
TASK 2: Graphical Representation of Data (10 marks)
Below is the number of international students studying in the United States from various countries in 2022.
| Country | Number of Students | Country | Number of Students |
|---|---|---|---|
| China | 290,000 | Canada | 27,000 |
| India | 240,000 | Vietnam | 26,000 |
| South Korea | 49,000 | Taiwan | 22,000 |
| Saudi Arabia | 37,000 | Mexico | 17,000 |
Instructions:
Use Excel to create a bar graph and a pie chart for the data above.
Which chart type better represents this dataset? Justify your answer with at least two reasons.
TASK 3: Normal Distribution & Probabilities (30 marks)
Choose a reliable secondary dataset (e.g., heights, weights, temperatures, incomes) from sources like Kaggle, Data.gov, or UCI Repository.
Use your selected dataset to demonstrate understanding of continuous probability distribution.
Instructions:
1. Check for normality using graphs or tests (e.g., histogram, Q-Q plot).
2. Transform the data to standard normal distribution (Z-scores).
3. Calculate and interpret the probability that a value falls within a specific range.
4. Calculate and interpret the confidence interval for the mean.
Include all calculations, charts, and interpretations.
TASK 4: Probability and Permutations (15 marks)
A cybersecurity analyst must guess a secure 6-digit password made of digits 0 to 9 with no repetition.
1. What is the probability of guessing the password correctly on the first try?
2. Assume the company changes the rule:
o Any permutation of the correct 6 digits is accepted.
o The analyst assumes one of the following combinations:
(a) All digits are unique
(b) One digit repeats twice
(c) Two digits repeat twice
(d) One digit repeats three times
Calculate the probability of guessing the correct 6-digit combination in each case. Show full steps and formula usage.
TASK 5: Data Collection, Descriptive & Inferential Analysis (40 marks)
Two NBA teams have been assigned to your group (Refer to the list given). Collect team stats from season 1990-91 to 2024-25 from: https://www.basketball-reference.com/teams/
Instructions:
1. Example: if one of the team is ‘Atlanta Hawks’ under FRANCHISE click ‘Atlanta Hawks’. You will see there are 76 seasons for this team. Click Share & Export and choose ‘Get as Excel Workbook’ to download the data.
2. Step 3 to 6 uses only Team 1 data.
3. Create a stem-and-leaf plot for ‘Wins’. Calculate median and mode. Interpret the results.
4. Build an ungrouped frequency table for number of wins. Calculate mean, variance, and standard deviation. Interpret the results. Plot a bar graph and pie chart.
5. Create a discrete probability distribution for ‘Wins’. Give examples for probability. Calculate mean, variance, and standard deviation and interpret the results. Compare with results from step 4 and discuss the results.
6. Create a grouped frequency distribution for “Wins”. Calculate the mean, median, mode, variance, and standard deviation. Draw a histogram and estimate the mode visually. Draw a cumulative frequency curve and estimate the median visually. Interpret all the results. Compare and discuss your results from step 5.
7. Construct a binomial distribution for wins and losses of Team 2 in the 2023-24 season. Give a few examples in finding probability. Compute mean, variance, and standard deviation. Interpret all the results.
8. Construct a Two-Way Classification Table comparing both teams’ wins and losses from the 2022-2023 season.
9. Using the Two-Way Classification Table:
(a) Are ‘Wins’ and ‘Team 2’ independent events?
(b) Are ‘Losses’ and ‘Wins’ mutually exclusive?
Explain and justify your answers.
| Group | Team 1 | Team 2 |
|---|---|---|
| 1 | Atlanta Hawks | Miami Heat |
| 2 | Boston Celtics | Milwaukee Bucks |
Your investigation will be assessed using the following assessment design criteria.
Marking Criteria for K17MA ASSIGNMENT JULY/SEPTEMBER 2024
| Concepts and Techniques | Reasoning and Communication |
|---|---|
| A 11-15 Comprehensive knowledge and understanding of concepts and relationships. Successful development and application of mathematical models to find concise and accurate solutions. Appropriate and effective use of electronic technology to find accurate solutions to routine and complex problems. |
Comprehensive interpretation of mathematical results in the context of the problem. Drawing logical conclusions from mathematical results, with a comprehensive understanding of their reasonableness and limitations. Highly effective communication of mathematical ideas and reasoning to develop logical and concise arguments. |
| B 9-10 Some depth of knowledge and understanding of concepts and relationships. Some development and successful application of mathematical models to find mostly accurate solutions. Mostly appropriate and effective use of electronic technology to find mostly accurate solutions to routine and some complex problems. |
Mostly appropriate interpretation of mathematical results in the context of the problem. Drawing mostly logical conclusions from mathematical results, with some depth of understanding of their reasonableness and limitations. Mostly effective development and testing of valid conjectures, with substantial attempt at proof. |
| C 6-8 Generally competent knowledge and understanding of concepts and relationships. Successful application of mathematical models to find generally accurate solutions. Generally appropriate and effective use of electronic technology to find mostly accurate solutions to routine problems. |
Generally appropriate interpretation of mathematical results in the context of the problem. Drawing some logical conclusions from mathematical results, with some understanding of their reasonableness and limitations. Development and testing of generally valid conjectures, with some attempt at proof. |
| D 4-5 Basic knowledge and some understanding of concepts and relationships. Some application of mathematical models to find some accurate or partially accurate solutions. Some appropriate use of electronic technology to find some accurate solutions to routine problems. |
Some interpretation of mathematical results. Drawing some conclusions from mathematical results, with some awareness of their reasonableness or limitations. Some communication of mathematical ideas, with attempted reasoning and/or arguments. |
| E 1-3 Limited knowledge or understanding of concepts and relationships. Attempted application of mathematical models, with limited accuracy. Attempted use of electronic technology, with limited accuracy in solving routine problems. |
Limited interpretation of mathematical results. Limited understanding of the meaning of mathematical results, their reasonableness or limitations. Attempted communication of mathematical ideas, with limited reasoning. |
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