Mean & Standard Deviation

The mean is the average of a set of numbers, calculated by adding all the numbers together and dividing by the count of numbers.

Mean = (5 + 11 + 2 + 12 + 4 + 2) / 6 = 6.

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

1. Find the mean of the data set. 2. Subtract the mean from each data point and square the result. 3. Find the average of those squared differences. 4. Take the square root of that average.

Population standard deviation uses the entire population for calculations, while sample standard deviation uses a sample of the population and divides by (n-1) instead of n.

σ = √(Σ(xi - μ)² / N), where μ is the population mean and N is the number of data points.

s = √(Σ(xi - x̄)² / (n - 1)), where x̄ is the sample mean and n is the number of data points.

Standard deviation = 6.89.

Standard deviation = 15.87.

A low standard deviation indicates that the data points tend to be close to the mean, showing less variability.