Mean & Standard Deviation

Front

What is the mean of a set of numbers?

Back

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

Front

How do you calculate the mean of the following numbers: 5, 11, 2, 12, 4, 2?

Back

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

Front

What is standard deviation?

Back

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

Front

How do you calculate the standard deviation of a data set?

Back

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.

Front

What is the difference between population standard deviation and sample standard deviation?

Back

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.

Front

What is the formula for population standard deviation?

Back

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

Front

What is the formula for sample standard deviation?

Back

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

Front

Given the data set {5, 10, 7, 12, 0, 20, 15, 22, 8, 2}, what is the standard deviation?

Back

Standard deviation = 6.89.

Front

Given the data set {12, 13, 29, 18, 61, 35, 21}, what is the standard deviation?

Back

Standard deviation = 15.87.

Front

What does a low standard deviation indicate about a data set?

Back

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