1. The problem is to identify the measure of dispersion and interpret bivariate data. 2. Measures of dispersion describe the spread or variability in a data set. Common measures include range, variance, and standard deviation. 3. Bivariate data involves two variables and their relationship. To interpret bivariate data, we often use correlation and regression analysis. 4. The formula for variance (a measure of dispersion) is: $$\text{Variance} = \sigma^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2$$ where $x_i$ are data points, $\mu$ is the mean, and $n$ is the number of data points. 5. The standard deviation is the square root of variance: $$\text{Standard Deviation} = \sigma = \sqrt{\frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2}$$ 6. For bivariate data, the correlation coefficient $r$ measures the strength and direction of a linear relationship: $$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$$ where $\bar{x}$ and $\bar{y}$ are means of $x$ and $y$. 7. Interpretation: - A small measure of dispersion means data points are close to the mean. - A large measure means data points are spread out. - Correlation $r$ close to 1 or -1 indicates strong linear relationship. - Correlation $r$ near 0 indicates weak or no linear relationship. This helps understand variability and relationships in data.