Standard deviation and Variance

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Variance is the average of the squared differences from the mean. It quantifies how much the numbers in a data set differ from the mean of the data set.

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

Approximately 99.7% of the data falls within three standard deviations of the mean in a normal distribution.

To calculate the mean, sum all the values in the data set and then divide by the number of values.

Variance (σ²) = Σ (xi - μ)² / N, where xi represents each value, μ is the mean, and N is the number of values.

Standard deviation (σ) = √(Variance). It is the square root of the variance.

The standard deviation is 7.26.

The variance is 47.47.