The standard deviation

Definition

The standard deviation is a measure of the amount of variation or dispersion in a set of values. It quantifies how much the individual data points deviate from the mean of the data set.

5 Must Know Facts For Your Next Test

1. The standard deviation is denoted by $\sigma$ when referring to a population and $s$ for a sample.
2. In hypothesis testing with two samples, known standard deviations are used to calculate the test statistic.
3. A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates more spread out data points.
4. When comparing two population means, the combined standard error incorporates both populations' standard deviations.
5. The formula for calculating the test statistic in this context is $Z = \frac{(\bar{X}_1 - \bar{X}_2)}{\sqrt{(\sigma_1^2 / n_1) + (\sigma_2^2 / n_2)}}$, where $\sigma_1$ and $\sigma_2$ are the known standard deviations.

Related terms

Mean:

The average value of a set of numbers, calculated by dividing the sum of all values by their count.

Variance:

A measure of how far each number in a data set is from the mean, calculated as the average squared deviation from the mean.

Standard Error:

An estimate of how much an observed sample mean would vary from its true population mean, often used in hypothesis testing.