Data Analysis & Scale Drawing

Name:

Date:

🎯 WALT: We Are Learning To

• Interpret scatter plots and identify correlation types

• Construct and analyse trend lines

• Calculate scale drawing dimensions accurately

• Apply statistical measures to real-world data

Success Criteria:

✓ I can identify positive, negative, and no correlation from scatter plots

✓ I can calculate scale factors and convert measurements

✓ I can draw appropriate trend lines and make predictions

📊 Part 1: Data Analysis & Correlation

1. A scatter plot shows the relationship between study hours and test scores. The points generally rise from left to right. What type of correlation is this?

Strong positive correlation

Weak negative correlation

No correlation

Strong negative correlation

2. The correlation coefficient (r) for temperature and ice cream sales is 0.85. This indicates:

Weak positive correlation

Strong positive correlation

Perfect negative correlation

No correlation

3. When drawing a line of best fit, which statement is most accurate?

The line must pass through every data point

The line should have roughly equal points above and below it

The line should only connect the first and last points

The line must be perfectly horizontal

4. Hinge Point Question: A trend line has the equation y = 2.5x + 10, where x is hours studied and y is test score. Predict the test score for someone who studies 6 hours.

📐 Part 2: Scale Drawing Applications

5. A school playground is 80 metres long. On a scale drawing using 1:400, what is the length on the drawing?

6. A building blueprint uses a scale of 1 cm : 2.5 m. If a room measures 4.8 cm on the blueprint, what is the actual length of the room?

7. Problem-Solving Challenge: A rectangular sports field measures 120m × 80m. You need to create a scale drawing that fits on A4 paper (29.7cm × 21cm) with 2cm margins on all sides. Calculate an appropriate scale factor and show your working.

8. Real-World Application: Explain why architects use scale drawings instead of drawing buildings at actual size. Give two practical reasons.

🚀 Differentiation & Extension

Support Strategy (Visual Learners): Draw a simple scatter plot showing the relationship between car age (years) and value ($). Use these points: (1, $25000), (3, $18000), (5, $12000), (7, $8000)

Extension Activity (Advanced Learners): Research and explain the difference between correlation and causation. Provide an example of two variables that are correlated but where one does not cause the other.

Exit Ticket: Rate your confidence (1-5) with today's learning objectives and identify one concept you'd like to revisit:

Interpreting scatter plots: _____ Scale calculations: _____ Trend line analysis: _____

I need more help with: _________________________________

🗝️ Answer Key

Part 1: Data Analysis & Correlation

1. Strong positive correlation - The points rising from left to right indicate that as study hours increase, test scores also increase.

2. Strong positive correlation - A correlation coefficient of 0.85 indicates a strong positive relationship between temperature and ice cream sales.

3. The line should have roughly equal points above and below it - This is the correct approach for a line of best fit.

4. For x = 6, y = 2.5(6) + 10 = 15. The predicted test score is 15.

Part 2: Scale Drawing Applications

5. Length on drawing = 80m / 400 = 0.2m or 20cm.

6. Actual length = 4.8cm * 2.5m = 12m.

7. Scale factor = (A4 dimensions - margins) / actual dimensions. The scale factor is calculated to fit the field within the A4 size.

8. Architects use scale drawings to accurately represent dimensions and to fit large structures on manageable paper sizes.

Differentiation & Extension

Support Strategy: Students should create a scatter plot based on the provided points, showing the decline in car value as age increases.

Extension Activity: Correlation indicates a relationship between two variables, while causation indicates that one variable directly affects the other. An example is the correlation between ice cream sales and temperature; higher temperatures correlate with increased ice cream sales, but one does not cause the other.