To calculate the sample variance, follow these steps:

1. Find the mean (average): $\text{Mean} = \frac{15 + 20 + 40 + 25 + 35}{5} = \frac{135}{5} = 27$

2. Calculate each data point's deviation from the mean (difference between each value and the mean) and square the result: $(15 - 27)^2 = (-12)^2 = 144$ $(20 - 27)^2 = (-7)^2 = 49$ $(40 - 27)^2 = (13)^2 = 169$ $(25 - 27)^2 = (-2)^2 = 4$ $(35 - 27)^2 = (8)^2 = 64$

3. Sum these squared deviations: $144 + 49 + 169 + 4 + 64 = 430$

4. Divide by $n - 1$ (where $n$ is the sample size, which is 5): $\text{Sample Variance} = \frac{430}{5 - 1} = \frac{430}{4} = 107.5$

Thus, the sample variance is 107.5.

Would you like more details or have any questions? Here are some related problems you could explore:

1. What is the standard deviation of this sample?
2. How would the variance change if an additional value was added to the dataset?
3. What is the population variance if this sample represents the entire population?
4. How does variance differ from standard deviation?
5. How can variance be used to understand data spread?

Tip: Variance provides an idea of how spread out the data is, but the square root (standard deviation) is more intuitive for understanding deviations from the mean in the original units.