Final answer:
- Variance is the average of squared deviations from the mean, while standard deviation is its square root, relating the two measures of spread.
- Variance equals zero when there is no variation in the data, which in terms of phenotypes, occurs when all individuals express the same traits.
Step-by-step explanation:
The variance and the standard deviation are related measures of spread within a set of data. Variance is mathematically defined as the average of the squared differences from the mean, while standard deviation is the square root of the variance. Due to this relationship, standard deviation is expressed in the original units of the data, and variance is expressed in those units squared.
The variance of a distribution of phenotypes, or any set of data, equals zero when there is no variability within the data. This occurs when all observations are identical. In biological terms, this would happen if every individual in a population had the exact same phenotype, meaning there is no diversity or difference in the expression of genetic characteristics.