Mathematics 10 — Exercise 11.1 · Q7

Full question

The table gives the scores of eight students in their first and second quizzes. Draw a scatter diagram, draw a line of best fit and describe the correlation between the two sets of scores.

Step-by-step solution

1. Each table column forms ONE ordered pair (x,y). Keep each pair together.

2. Label the horizontal and vertical axes, choose uniform scales, then plot every pair.

3. Draw a straight line through the middle of the point cloud, with points on both sides. This is an estimate; different sensible hand-drawn lines give slightly different predictions.

4. Strong positive correlation: y tends to rise as x rises.

5. For reproducible estimates the drawn line uses least squares. Its slope is Σ(x−x̄)(y−ȳ)/Σ(x−x̄)²; intercept is ȳ−slope×x̄.

   $$y=\frac{6282\times x}{7559}+\frac{19688}{7559}$$

Answer

Strong positive correlation.