What formula is used to calculate the variance of a population?

What formula is used to calculate the variance of a population?

• A. sum(x - mean)^2 / N
• B. sum(x - samplemean)^2 / n - 1
• C. (x - mean) / N
• D. sum(x) / N

Answer: (A)

The formula for calculating the variance of a population is indeed represented by summing the squared differences between each data point and the population mean, then dividing that sum by the number of data points in the population (N). This approach effectively captures the extent to which each data point deviates from the average, providing a measure of the spread of the data within the entire population. The squaring of the differences ensures that negative and positive deviations do not cancel each other out. The division by N indicates that you are considering the entire population for this calculation, which is crucial for obtaining the population variance. In contrast, other options provided in the question utilize different approaches or definitions of variance. One refers to the sample mean and applies a correction factor (n - 1) to account for the bias in estimating population variance from a sample, which is used in calculating the sample variance instead. The other options describe calculations that either do not yield variance or use incorrect formulas, leading to invalid results in the context of population variance.

The formula for calculating the variance of a population is indeed represented by summing the squared differences between each data point and the population mean, then dividing that sum by the number of data points in the population (N).

This approach effectively captures the extent to which each data point deviates from the average, providing a measure of the spread of the data within the entire population. The squaring of the differences ensures that negative and positive deviations do not cancel each other out. The division by N indicates that you are considering the entire population for this calculation, which is crucial for obtaining the population variance.

In contrast, other options provided in the question utilize different approaches or definitions of variance. One refers to the sample mean and applies a correction factor (n - 1) to account for the bias in estimating population variance from a sample, which is used in calculating the sample variance instead. The other options describe calculations that either do not yield variance or use incorrect formulas, leading to invalid results in the context of population variance.