11-15-2025, 05:18 PM
Chapter 17 — Data Interpretation & Real-World Decisions
Data is everywhere:
• school reports
• scientific studies
• sports performance
• business trends
• medical results
• news headlines
• social media infographics
But raw numbers alone mean very little.
This chapter teaches you how to *interpret* data like a scientist —
spotting patterns, predicting behaviour, and avoiding common misunderstandings.
---
17.1 What Data Interpretation Really Means
Data interpretation means:
turning numbers into conclusions.
It means answering questions like:
• What is this data showing?
• Why might the numbers look like this?
• Are there patterns or trends?
• What predictions can we make?
• Is the conclusion trustworthy?
This is the skill examiners LOVE to test.
---
17.2 Trend Analysis — What Is Happening Over Time?
When data is shown over time, look for:
• upward trends
• downward trends
• periodic cycles
• sudden spikes
• unusual dips
• stable or flat patterns
Examples:
• exam scores improving year by year
• rainfall decreasing over decades
• population growth slowing down
• temperature spikes during summer
Understanding trends = understanding behaviour.
---
17.3 Spotting Patterns
Patterns include:
• linear increase/decrease
• exponential growth
• repeating cycles
• clustering of points
• sudden breaks in pattern
Example:
A student studies 2 more hours each week → scores rise steadily (linear).
A pandemic graph might show exponential growth.
Seasonal sales form yearly cycles.
Pattern recognition is the foundation of prediction.
---
17.4 Comparing Two Data Sets
Often you are shown:
• two graphs
• two bars
• two lines
• two tables
Things to compare:
• which is bigger?
• which changes faster?
• which is more stable?
• which has greater variation?
• where do they intersect?
Example:
Two companies’ profits over 10 years → which one is growing faster?
---
17.5 Interpreting Scatter Graphs
Scatter graphs show:
• how two variables relate
• whether the relationship is strong or weak
• whether it’s positive or negative
Examples:
• Hours revised vs test score → positive correlation
• Speed vs fuel efficiency → negative correlation
• Shoe size vs intelligence → no correlation
Remember:
Correlation does NOT mean causation.
---
17.6 Outliers — The Unusual Values
Outliers are values that don’t fit the pattern.
Example:
Reaction times: 260, 270, 265, 900
Outlier = 900 (someone pressed the button late)
Outliers may indicate:
• errors
• unusual events
• special cases
• measurement problems
Do NOT ignore them — ask why they happened.
---
17.7 Context Matters
Data NEVER exists alone.
You MUST consider:
• when it was collected
• who collected it
• how it was collected
• what might influence the results
Example:
Sales drop in December?
Context: company sells school uniforms.
Context changes interpretation completely.
---
17.8 Making Predictions
Exams often ask:
“Estimate the value in 2028…”
Use the pattern to extend your estimate.
Rules:
• never extend too far
• use the existing trend
• consider whether the trend is stable
Example:
Population increases by 200 per year, steadily → add 200.
---
17.9 Two Common Exam Questions
Question Type #1 — Describe the trend
“Sales increased until 2018, then decreased slightly, then levelled off.”
Question Type #2 — Compare two sets of data
“Group A has higher values overall and shows less variation than Group B.”
Vocabulary examiners love:
• increases
• decreases
• fluctuates
• plateau
• peaks
• dips
• rises sharply
• gradual decline
• more variation
• strong correlation
Using the right words = high marks.
---
17.10 Interpreting Bar Charts
Look for:
• which bar is highest
• differences between bars
• large changes → comment on them
• whether scale is fair
• which groups perform best or worst
Example:
“Year 9 has the lowest attendance, significantly below the others.”
---
17.11 Interpreting Line Graphs
Look for:
• slope (steep or gentle)
• direction
• turning points
• smoothness vs volatility
Example:
“The line rises steadily from Jan to Apr, then peaks in May, then declines sharply.”
---
17.12 When Predictions Are Dangerous
Be careful when:
• data is unstable
• only a few points exist
• trend changes suddenly
• external factors are unknown
Example:
Stock prices fluctuate wildly → prediction highly unreliable.
---
17.13 Exam-Style Questions
1. A line graph shows heart rate rising steadily during exercise, then levelling off.
Describe the pattern.
2. A scatter graph shows a strong positive correlation.
Explain what this means.
3. Two factories produce goods with these SDs:
Factory A: SD = 1.2
Factory B: SD = 3.7
Which is more consistent?
4. A bar chart shows rainfall:
Jan 30mm, Feb 20mm, Mar 60mm.
Describe what happened.
5. A scatter graph shows no correlation.
What does this tell you about the relationship between the variables?
---
17.14 Chapter Summary
• Data interpretation is the art of reading what data REALLY means
• Trends show behaviour over time
• Patterns help make predictions
• Scatter graphs show relationships
• Outliers need explanation
• Context matters
• Use precise mathematical language
• Always compare, describe, and explain
You now think like a real statistician —
ready for the final parts of the course.
---
Written and Compiled by Lee Johnston — Founder of The Lumin Archive
Data is everywhere:
• school reports
• scientific studies
• sports performance
• business trends
• medical results
• news headlines
• social media infographics
But raw numbers alone mean very little.
This chapter teaches you how to *interpret* data like a scientist —
spotting patterns, predicting behaviour, and avoiding common misunderstandings.
---
17.1 What Data Interpretation Really Means
Data interpretation means:
turning numbers into conclusions.
It means answering questions like:
• What is this data showing?
• Why might the numbers look like this?
• Are there patterns or trends?
• What predictions can we make?
• Is the conclusion trustworthy?
This is the skill examiners LOVE to test.
---
17.2 Trend Analysis — What Is Happening Over Time?
When data is shown over time, look for:
• upward trends
• downward trends
• periodic cycles
• sudden spikes
• unusual dips
• stable or flat patterns
Examples:
• exam scores improving year by year
• rainfall decreasing over decades
• population growth slowing down
• temperature spikes during summer
Understanding trends = understanding behaviour.
---
17.3 Spotting Patterns
Patterns include:
• linear increase/decrease
• exponential growth
• repeating cycles
• clustering of points
• sudden breaks in pattern
Example:
A student studies 2 more hours each week → scores rise steadily (linear).
A pandemic graph might show exponential growth.
Seasonal sales form yearly cycles.
Pattern recognition is the foundation of prediction.
---
17.4 Comparing Two Data Sets
Often you are shown:
• two graphs
• two bars
• two lines
• two tables
Things to compare:
• which is bigger?
• which changes faster?
• which is more stable?
• which has greater variation?
• where do they intersect?
Example:
Two companies’ profits over 10 years → which one is growing faster?
---
17.5 Interpreting Scatter Graphs
Scatter graphs show:
• how two variables relate
• whether the relationship is strong or weak
• whether it’s positive or negative
Examples:
• Hours revised vs test score → positive correlation
• Speed vs fuel efficiency → negative correlation
• Shoe size vs intelligence → no correlation
Remember:
Correlation does NOT mean causation.
---
17.6 Outliers — The Unusual Values
Outliers are values that don’t fit the pattern.
Example:
Reaction times: 260, 270, 265, 900
Outlier = 900 (someone pressed the button late)
Outliers may indicate:
• errors
• unusual events
• special cases
• measurement problems
Do NOT ignore them — ask why they happened.
---
17.7 Context Matters
Data NEVER exists alone.
You MUST consider:
• when it was collected
• who collected it
• how it was collected
• what might influence the results
Example:
Sales drop in December?
Context: company sells school uniforms.
Context changes interpretation completely.
---
17.8 Making Predictions
Exams often ask:
“Estimate the value in 2028…”
Use the pattern to extend your estimate.
Rules:
• never extend too far
• use the existing trend
• consider whether the trend is stable
Example:
Population increases by 200 per year, steadily → add 200.
---
17.9 Two Common Exam Questions
Question Type #1 — Describe the trend
“Sales increased until 2018, then decreased slightly, then levelled off.”
Question Type #2 — Compare two sets of data
“Group A has higher values overall and shows less variation than Group B.”
Vocabulary examiners love:
• increases
• decreases
• fluctuates
• plateau
• peaks
• dips
• rises sharply
• gradual decline
• more variation
• strong correlation
Using the right words = high marks.
---
17.10 Interpreting Bar Charts
Look for:
• which bar is highest
• differences between bars
• large changes → comment on them
• whether scale is fair
• which groups perform best or worst
Example:
“Year 9 has the lowest attendance, significantly below the others.”
---
17.11 Interpreting Line Graphs
Look for:
• slope (steep or gentle)
• direction
• turning points
• smoothness vs volatility
Example:
“The line rises steadily from Jan to Apr, then peaks in May, then declines sharply.”
---
17.12 When Predictions Are Dangerous
Be careful when:
• data is unstable
• only a few points exist
• trend changes suddenly
• external factors are unknown
Example:
Stock prices fluctuate wildly → prediction highly unreliable.
---
17.13 Exam-Style Questions
1. A line graph shows heart rate rising steadily during exercise, then levelling off.
Describe the pattern.
2. A scatter graph shows a strong positive correlation.
Explain what this means.
3. Two factories produce goods with these SDs:
Factory A: SD = 1.2
Factory B: SD = 3.7
Which is more consistent?
4. A bar chart shows rainfall:
Jan 30mm, Feb 20mm, Mar 60mm.
Describe what happened.
5. A scatter graph shows no correlation.
What does this tell you about the relationship between the variables?
---
17.14 Chapter Summary
• Data interpretation is the art of reading what data REALLY means
• Trends show behaviour over time
• Patterns help make predictions
• Scatter graphs show relationships
• Outliers need explanation
• Context matters
• Use precise mathematical language
• Always compare, describe, and explain
You now think like a real statistician —
ready for the final parts of the course.
---
Written and Compiled by Lee Johnston — Founder of The Lumin Archive