1. The problem is to understand how to create and interpret a scatter diagram, which is a graphical representation of two variables to identify any relationship between them. 2. A scatter diagram plots points on a Cartesian plane where each point represents paired data values $(x, y)$. 3. The formula for each point is simply the coordinate pair: $$ (x_i, y_i) $$ where $x_i$ and $y_i$ are the values of the two variables. 4. Important rules: - Each point corresponds to one observation. - Look for patterns such as clusters, trends (positive or negative correlation), or outliers. 5. To create a scatter diagram: - Collect paired data. - Plot each pair as a point on the graph. 6. Interpretation: - If points tend to rise from left to right, there is a positive correlation. - If points tend to fall from left to right, there is a negative correlation. - If points are scattered randomly, there is no correlation. 7. Example: Suppose we have data pairs $(1,2), (2,3), (3,5), (4,4), (5,6)$. - Plot these points on the graph. - Observe the trend: points generally increase, indicating a positive correlation. 8. Scatter diagrams are useful in statistics and data analysis to visually assess relationships between variables.