1. **Problem Statement:** Find the variance of the given data distribution shown on the graph. 2. **Understanding Variance:** Variance measures how spread out the data points are from the mean. For a normal distribution, variance is the square of the standard deviation. 3. **Given Data:** The graph is centered approximately at $x=4$, which is the mean ($\mu$). 4. **Interpreting the Graph:** The vertical dotted lines at about $3.7$, $4$, and $4.3$ suggest the spread around the mean. 5. **Estimating Standard Deviation ($\sigma$):** The distance from the mean to one of the dotted lines (e.g., from $4$ to $3.7$ or $4.3$) is approximately $0.3$. 6. **Calculating Variance:** Variance $= \sigma^2 = 0.3^2 = 0.09$. 7. **Matching to Options:** The closest option to $0.09$ is $0.0625$ (which is $0.25^2$), $0.25$, $0.5$, and $1.5$. Since the graph is bell-shaped and the variance is small, the best estimate is $0.25$. **Final answer:** The variance of the data is $0.25$.