What is the relationship between the variance and the standard deviation for a sample data set?

Soluion:

Basically, a data set is a collection of data, and data in this set is normally presented in a tabular pattern.

The relationship between the variance and the standard deviation for a sample data set is given below:

• Variance represents the average squared deviations from the mean value of data, while standard deviation represents the square root of that number.
• Both, the variance and the standard deviation measures variability in a distribution.
• Both have different units like the standard deviation has the same units as the original values like minutes or meters while the variance has much larger units like meters squared.
• The variance is equal to the square of standard deviation or the standard deviation is the square root of the variance.

Generally, "the variance is equal to the square of the standard deviation" is widely used as the relationship between the variance and the standard deviation for a sample data set.

So, according to the formula,

Variance = Square of Standard Deviation or
V = σ²
Where, V = Variance and σ = Standard Deviation

Hence, the variance is equal to the square of standard deviation.

What is the relationship between the variance and the standard deviation for a sample data set?

Summary:

The variance for a sample data set is equal to the square of standard deviation.