Variance and Standard Deviation Relationship

E

The variance is the mean of the squared deviations from the mean. The standard deviation is the positive square root of the variance.

The relationship between variance and standard deviation is as follows:

The variance is a measure of how spread out the values in a data set are. It is calculated by taking the average of the squared deviations from the mean. In other words, the variance is the average of the squared differences between each data point and the mean.

On the other hand, the standard deviation is a measure of the amount of variation or dispersion in a data set. It is simply the square root of the variance. The standard deviation is useful because it is expressed in the same units as the original data, whereas the variance is expressed in squared units.

To summarize:

1. Variance: The variance is calculated by taking the average of the squared differences between each data point and the mean. It gives us a measure of how spread out the data points are. The formula for variance is:

Variance = (Σ(xᵢ - x̄)²) / n

Where:

• xᵢ represents each individual data point
• x̄ represents the mean of the data set
• Σ represents the summation (i.e., adding up all the terms)
• n represents the number of data points

2. Standard Deviation: The standard deviation is the square root of the variance. It provides a measure of the average amount by which data points deviate from the mean. The formula for standard deviation is:

Standard Deviation = √(Variance)

Therefore, the correct answer to the question is E. "Variance is the square of the standard deviation." The variance is the square of the standard deviation, not the other way around.