Mayfield High School

Introduction

In the last few lessons, you have learnt all the skills you need for analysing: 

1. Bivariate (2 sets of data) data - finding a correlation, plotting a scatter graph, fitting a line of best fit 

2. Continuous univariate data - using frequency table, calculating and estimating averages, drawing histogram, frequency polygon and cumulative frequency graph

Let's take a moment to reflect on the following question: How does the representation of data  (e.g. scatter graph, histogram, grouped frequency table) influence the way we communicate findings?

1. When do we use each graph or table?  How do they make it easier to understand the data?

2. When is it NOT appropriate to use these?  How do they lead to confusion?

Writing a statistical report

In today's lesson, you are going to write a statistical report on the Mayfield High School data (MAKE A COPY OF ME).  

Competencies - communication

As you write your report, think about whether you are able to communicate effectively:

1. "I am aware of the different formats of communication and can express myself in different ways."
   For your report, this means: You know that a report isn't just a wall of text. You can use things like headings, bullet points, tables, and graphs to share your findings in different ways.

2. "I can communicate in a clear and connected manner making it easy for audiences to understand what I am trying to express."
   For your report, this means: Your sentences and paragraphs flow logically. Someone reading your report can easily follow your thoughts from your hypothesis, to your data, to your conclusions without getting confused.

3. "I can use different tools and processes to express myself clearly in multiple ways."
   For your report, this means You're comfortable using tools like a word processor (e.g., Google Docs) to write your text and a spreadsheet program (e.g., Google Sheets) to create your tables, calculate your stats and make your graphs. You use these tools to make your points clear.

4. "I can persuasively articulate my personal ideas so that it has an impact on others and generate positive change."
   For your report, this means: Your conclusions and recommendations are convincing. You use the evidence from your data to back up your points so that the School Board understands why your findings are important and feels motivated to consider your suggestions.

5. "I can comfortably use technology/media to work efficiently, create authentic products, and communicate effectively with others."
   For your report, this means: You can use your computer and software (like Google Docs and Sheets) smoothly to put together a professional-looking report. You can easily include your graphs and tables, making your report accurate and easy to share.

What to include in your report

In your report, please include these sections:

1. Introduction (1st paragraph)
   Explain what your project is about so that someone reading it for the first time can understand what you are doing.

You can use these sentence starters:

• "The focus of my project is…"

• "I am going to investigate whether…"

2. Hypothesis (2nd paragraph)
   This is your guess about what you think the information will show.

For example:
    You might think that students who sleep more will score higher marks in their exams. This is your hypothesis.

You can use these sentence starters:

• "The hypotheses I will be testing are…"

• "I think that…"

• "I believe this is true because…"

3. Plan of Action (3rd paragraph)
    Explain how you plan to carry out your project.

You can use these sentence starters:

• "I will need to group my data because…"

• "I will group it by…"

• "The calculations I plan to do are…"

• "I will do most of the calculations… (by hand or on the computer?)"

• "I hope the results will show…"

• "The diagrams and graphs I plan to draw are…"

• "I hope each diagram will show…"

4. Analysis of Data
    This is where you write down your calculations and draw diagrams.

• Calculations can include: mean, median, mode, range, interquartile range, variance, and correlation coefficient.

• Diagrams can include: bar charts, pie charts, scatter diagrams, histograms, and cumulative frequency graphs.

IMPORTANT: If you use Google Sheets, it can help you with calculations and diagrams, but don’t include something just because it’s easy. You must include at least 1 scatter diagram and its "r" value!

5. Interpretation (4th paragraph)
    Explain what your diagrams and statistics show about your hypothesis.

• For example, your scatter graph will help you determine correlation to prove or disprove your hypothesis.

You can use these sentence starters:

• "The results of my calculations show…"

• "The diagram/graph shows…"

• "This supports my hypothesis because…"

6. Conclusion
    Summarize what you found out and how you could improve your project.

You can use these sentence starters:

• "Overall, my project proves/disproves my original hypothesis."

• "I say this because…"

• "I believe my sample was/wasn’t large enough…"

• "If I did this investigation again, I would…"

• "I could develop my investigation by…"

Note: it is quality NOT quantity that matters! A shorter piece that addresses the task is better than a large amount of work that contains many irrelevant calculations or diagrams.

If you have forgotten how to do any of the calculations or diagram, take a look at: https://gcseguide.co.uk/maths/statistics/ 

Further Support: Sample Statistical Report - Screen Time and Academic Performance

The sample below is focused on screen time and academic performance.  Take a look and follow the format to investigate other variables.

Anything in red is enrichment i.e. beyond what you need to know for Year 8.

Introduction: What This Project is About

This project investigates the relationship between the amount of time students spend on screens each week (such as phones, computers, and tablets) and their academic performance in school. The main goal is to determine if there is a clear connection between these two factors. Essentially, this report aims to see if significant screen use affects how well students perform in their schoolwork, by presenting the collected information, the methods used to analyze it, and an explanation of the findings.

Hypothesis: What I Expect to Find

The hypothesis I am testing is that there is a negative correlation between the weekly hours students spend on screens and their academic performance percentage. This means I predict that as screen time increases, academic grades might decrease. I believe this could be true because extensive screen time might reduce the time available for homework and studying. Furthermore, high screen usage could lead to distractions or impact sleep quality, which in turn could negatively affect concentration and academic results.

Plan of Action: How I Will Conduct the Investigation

To test my hypothesis, I will analyze the data provided by the school on student screen time and academic grades. I will need to organize the data into groups for variables like 'Screen Time' (e.g., 0 ≤ screen time < 5 hours, 5 ≤ screen time < 10 hours, etc.) and 'Academic Performance' (e.g., 0% ≤ grade < 10%, 10% ≤ grade < 20%, etc.). This grouping will help in creating histograms to understand the distribution of the data.

The statistical calculations I plan to perform include:

• Determining the average (mean), the middle value (median), and the most frequent value (mode) for both screen time and academic grades. I will also calculate the range to see how spread out the data is.

• Identifying the estimated average and the most common group from the grouped frequency tables.

• Calculating the correlation coefficient ('r'), a statistical measure that indicates the strength and direction (positive or negative) of the linear relationship between screen time and grades.

• Finding the equation for the line of best fit on the scatter graph and the R² value (coefficient of determination), which helps explain how much of the change in one variable can be attributed to the other.

I will use computer software, such as Googlesheets, for most of these calculations to ensure accuracy and efficiency. I hope the results of these calculations will clearly illustrate typical screen time usage and academic performance levels and, more importantly, reveal the nature and strength of any relationship between them.

The statistical diagrams I plan to create are:

• A histogram for ‘Screen Time (hours/week)’.

• A histogram for ‘Academic Performance (%)’.

• A scatter graph plotting ‘Academic Performance (%)’ against ‘Screen Time (hours/week)’, which will include a line of best fit.

I expect these diagrams to show:

• The histograms will provide a visual representation of how screen time and academic performance are distributed among the students, highlighting common ranges and any patterns in the data.

• The scatter graph will visually demonstrate whether increased screen time generally corresponds with higher or lower academic performance, and how closely the data points align with a linear trend.

The initial summary statistics showed that the average screen time for students is approximately 13.47 hours per week, with the median being 13 hours. The average academic performance is 49.43%, with a median of 48%. The most common (mode) screen time was 23 hours, while the most common grade was 15%. Both screen time and academic performance show a wide range (28 hours and 96 percentage points, respectively), indicating significant variation among the students.

Interpretation of Grouped Information and Histograms:

The histogram for screen time revealed that the most common group (modal group) was 10 ≤ screen time < 15 hours per week. However, a substantial number of students (20) also reported 20 ≤ screen time < 25 hours. This suggests that while moderate screen time is frequent, a considerable portion of students engage in higher levels of screen use.

The histogram for academic performance indicated that the modal group was students scoring between 10% ≤ grade < 20%. The grades are distributed across all performance levels, with another noticeable group achieving 90% ≤ grade < 100%, highlighting diverse academic outcomes.

Interpretation of Scatter Graph:

The scatter graph, which plots academic performance against screen time, clearly illustrates a negative trend. As screen time increases (moving to the right on the graph), academic performance generally tends to decrease (the plotted points tend to go downwards). The line of best fit, which is drawn through the data points, has a negative slope (-2.18). This mathematically confirms the observed negative relationship. The equation for this line (Grades (%) = -2.18 x (Screen Time) + 78.8) suggests that, on average, for each additional hour of screen time per week, a student's academic performance is predicted to decrease by approximately 2.18 percentage points.

The correlation coefficient (r) is -0.5879. This value signifies a moderate negative linear correlation between screen time and academic performance. The "negative" aspect means that as one variable (screen time) increases, the other variable (academic performance) tends to decrease. A value of approximately -0.59 is considered a moderate correlation, indicating a noticeable but not perfect linear relationship. The R² value (coefficient of determination) is 0.346. This means that about 34.6% of the differences observed in academic performance can be attributed to differences in weekly screen time. While this is a significant portion, it also indicates that other factors (approximately 65.4%) influence academic performance.

These findings provide strong support for my initial hypothesis that increased screen time is linked to lower academic performance. Both the visual trend in the scatter graph and the calculated correlation coefficient confirm this relationship.

Conclusion: So, What’s the Bottom Line?

Overall, this investigation demonstrates that the original hypothesis is supported: there is a negative relationship between the number of hours students spend on screens weekly and their academic grades. This conclusion is based on the scatter graph, which showed a clear downward trend, and the correlation coefficient of -0.5879, indicating a moderate-strength negative linear link. The equation of the line of best fit also showed that more screen time generally corresponds to lower predicted grades.

The sample of 100 students provides a reasonable basis for these findings for this particular group. However, to make broader generalizations (e.g., to all students in a region), a larger and more varied sample might be necessary. Since the findings aligned with the initial hypothesis, the hypothesis was not changed.

If this investigation were to be conducted again, several improvements could be made:

• Collect data from a larger and more diverse group of students to enhance the reliability and generalizability of the results.

• Gather more specific information about the type of screen time (e.g., educational activities, social media, gaming), as different uses might have varying impacts on academic performance.

• Include other potentially relevant variables, such as hours spent studying, sleep duration, socioeconomic factors, and parental involvement, to develop a more comprehensive understanding of the factors influencing academic success.

To further develop this investigation, one could:

• Conduct a longitudinal study, tracking the same students over an extended period to observe how changes in screen time habits correlate with changes in their academic performance over time.

• Explore if the relationship between screen time and academic performance is non-linear, meaning the effect might change at different levels of screen time (e.g., a small amount of screen time might have little impact, while very high levels have a more significant effect).

• Attempt to identify if there are specific thresholds of screen time beyond which the negative impact on academic performance becomes more pronounced.