Standard deviation and Variance

Front

What is standard deviation?

Back

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.

Front

What is variance?

Back

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.

Front

What percent of data falls within one standard deviation of the mean in a normal distribution?

Back

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

Front

What percent of data falls within two standard deviations of the mean in a normal distribution?

Back

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

Front

What percent of data falls within three standard deviations of the mean in a normal distribution?

Back

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

Front

How do you calculate the mean of a data set?

Back

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

Front

What is the formula for variance?

Back

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

Front

What is the formula for standard deviation?

Back

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

Front

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

Back

The standard deviation is 7.26.

Front

Given the data set: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2, what is the variance?

Back

The variance is 47.47.