1. **State the problem:** Given a sample size $n=100$, mean $\mu=40$, and standard deviation $\sigma=3$, find the sum of squared deviations from the mean. 2. **Formula used:** The sum of squared deviations (also called the sum of squares) is given by: $$\text{Sum of squares} = \sum_{i=1}^n (x_i - \mu)^2$$ 3. **Important rule:** The variance $\sigma^2$ is the average of these squared deviations: $$\sigma^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2$$ 4. **Calculate variance:** Since standard deviation $\sigma=3$, variance is: $$\sigma^2 = 3^2 = 9$$ 5. **Find sum of squares:** Multiply variance by $n$: $$\sum_{i=1}^n (x_i - \mu)^2 = n \times \sigma^2 = 100 \times 9 = 900$$ **Final answer:** The sum of squared deviations is $900$.