Mathematics IA

Topic 1: Developing a modelling to predict the crime rate based on some socioeconomic factors.

Research question 1: What is the correlation between crime rates and socioeconomic factors such as unemployment and poverty?

Socioeconomic factors:

· Poverty -> GDP ranking: discuss how GDP rankings can serve as an indicator of poverty levels and its potential impact on crime rates.

· Unemployment: analyze the relationship between unemployment rates and crime & consider how higher unemployment may correlate with increased crime rates.

Personal connection:

· Interested in this topic: my motivation for studying crime rates and socioeconomic factors.

· Future aspirations: mention my plans to study crime-related courses at uni & how this research contributes to my academic pathway.

Potential impact:

1, Public policy and resource allocation guide decision-making.

· Policymakers can be based on this resources and target area with higher predicted crime rates for preventive measures.

· Ex: Increase job training / increase educational support

è Attracting investment -> to offer more job opportunities.

the potential benefits of job training programs and educational support aimed at reducing poverty and unemployment.

2, academic and research contributions

è Further research directions

How my findings could encourage further studies into the relationship between socioeconomic factors and crime.

DATA:

Topic 10 countries with the highest crime rates in 2024 (https://worldpopulationreview.com/country-rankings/crime-rate-by-country)

Crime index:

GOCI: The GOCI indicates countries' ability to deal with organised crime and their vulnerability to organised crime, and ranks each country based on these two factors.

Topics and Methodology

1. Scatter plot (SL)

2. Regression line (SL)

3. Pearson’s product-moment correlation coefficient r -> (SL)

4. Non-linear regression (HL)

5. Hypothesis testing (Chi-square independent test to stat) (HL)

6. Looking at Statistics from a sample of the data set. (HL)

7. Passion distribution

8.

1. Scatter plot (SL):

· Data collection: gather data on crime rates, unemployment rates, and poverty levels (potentially using GDP rankings as a proxy for poverty)

· Visual representation: create a scatter plot to visualize the relationship between crime rates and each socioeconomic factor.

·  Analysis: identify the correlation and draw a regression line. Calculate means for relevant data point.

Scatter plot (use GDC) to draw graph -> find correlation and regression line -> find the mean

(if correlation doesn’t match -> non-linear correlation -> use residual plot (HL)

2. Regression line (SL):

· Model development: fit a regression line to ur scatter plot data for both unemployment and poverty.

· Interpretation: discuss the meaning of the slope and y-intercept in the context of crime prediction.

3. Pearson’s product-moment correlation coefficient r -> (SL)

· Calculation: compute Pearson’s r for the relationships between crime rates and both unemployment and poverty.

· Interpretation: analyze the correlation coefficients to determine the strength and direction of the relationships.

4. Non-linear regression (HL):

· Exploration of non-linearity:

5. Chi-square independent test (dependent or independent) – hypothesis test

- It is a test that measures how a model compares to actual observed data.

· Unemployment & poverty -> crime rate

Structure

1. Introduction

Context: Briefly introduce crime rates and their significance.

Research Question: Clearly state your research question: What is the correlation between crime rates and socioeconomic factors such as unemployment and poverty?

Personal Connection: Discuss your interest and motivations for selecting this topic, along with future aspirations in crime-related studies.

2. Literature Review

Socioeconomic Factors:

Poverty: Discuss GDP rankings as an indicator of poverty and its implications for crime rates.

Unemployment: Analyze literature on the relationship between unemployment rates and crime rates.

3. Methodology

Data Collection: Describe how you will gather data on crime rates, unemployment rates, and poverty levels (e.g., using GDP).

Statistical Tools: Outline the mathematical concepts and tools you will use, such as:

Scatter plots

Regression lines

Pearson’s correlation coefficient

Non-linear regression

Chi-square independence testing

4. Analysis

Scatter Plot (SL):

Present and analyze scatter plots to visualize relationships.

Discuss correlation and regression lines; calculate means of relevant data points.

Regression Analysis (SL):

Fit regression lines and interpret coefficients (slope and y-intercept) in the context of your research.

Pearson’s Correlation Coefficient (SL):

Calculate and interpret Pearson's r for both unemployment and poverty against crime rates.

Non-linear Regression (HL):

Explore non-linear relationships and analyze residuals.

Chi-Square Test (HL):

Conduct a hypothesis test to compare observed crime rates with expected rates based on socioeconomic factors.

5. Evaluation

Interpretation of Results: Discuss findings from your analysis, including implications for understanding the relationship between crime and socioeconomic factors.

Potential Impact:

Public Policy: How your findings can guide policymakers in resource allocation and preventive measures.

Academic Contributions: Suggest directions for further research based on your findings.

6. Conclusion

Summary of Findings: Recap the main results and their significance.

Reflection: Reflect on the research process and what you learned about the relationship between socioeconomic factors and crime.

7. References

List all sources used for data collection and literature review.

Additional Topics from the Syllabus

Descriptive Statistics: Discuss measures of central tendency and dispersion for your data sets.

Probability Distributions: Explore how different distributions (e.g., normal distribution) might apply to your data.

Statistical Inference: Discuss confidence intervals or hypothesis testing in the context of your findings.

Data Visualization: Consider using other forms of data visualization, such as histograms or box plots, to present your findings.