ybar2

Ybar2 is a notation used in statistics and data analysis to denote a mean associated with the second variable or the second group in a dataset. The exact interpretation depends on context, but the common idea is that ybar2 represents an average value computed from a specified subset of data or a second variable.

Definition and calculation

If there are n2 observations in the second group or for the second variable, with values y_{1,2}, y_{2,2}, ..., y_{n2,2}, then ybar2 is defined as the sample mean: ybar2 = (1/n2) times the sum of y_{i,2} for i from 1 to n2. In multi-variable data where you summarize each variable by its mean, ybar2 may refer to the mean of the second variable across all observations, forming part of a vector of means like (ybar1, ybar2, ...).

Context and usage

In a two-group comparison, ybar2 often denotes the mean of the outcome within group 2. It is commonly used in formulas for between-group variation, contrasts, and in computing the overall mean as a weighted combination of group means: ybar = (n1*ybar1 + n2*ybar2) / (n1 + n2). In a multivariate context, ybar2 can simply be the second component of the vector of sample means, representing the average of the second variable across the dataset.

Examples

If group 2 has observations 5, 7, and 6, then ybar2 = (5 + 7 + 6) / 3 = 6.

See also

y-bar, sample mean, population mean, group mean, between-group variation.