In the context of probability, an outcome refers to a possible result of a random experiment. For example, if the experiment is tossing a coin, the possible outcomes are 'Heads' or 'Tails'. Each outcome is considered mutually exclusive, meaning only one outcome can occur at a time.

The type of data that describes attributes or characteristics of a group is called Qualitative data. These are often non-numeric and may include data types such as text, audio, or video. Examples include a person's gender, eye color, or the make of a car.

The assumption of normality in residual analysis states that if we draw a large number of samples and create a distribution of the sample means, this distribution will be well approximated by a normal distribution. This is necessary to make inferences about the regression coefficients and to calculate prediction intervals.

In the Wilcoxon Signed Rank Test, zeros in the difference of paired observations are typically discarded.

The primary purpose of ANOVA (Analysis of Variance) is to test if there is any statistically significant difference between the means of three or more groups.

Increasing the sample size makes the test more sensitive, thereby reducing both Type I and Type II errors. With a larger sample, there is more data available, which often leads to more accurate and reliable results. However, resources, time, and other constraints often limit the sample size in real-world studies.

The Central Limit Theorem (CLT) states that the distribution of sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the population distribution. Therefore, the CLT has a profound impact on the shape of the distribution, tending to 'normalize' it as sample size increases.

Each subsequent Principal Component in PCA must be orthogonal (perpendicular) to all previous Principal Components. This ensures that the Principal Components are uncorrelated.

The assumptions of factor analysis include normality (the variables used in the analysis should be normally distributed), linearity (the relationship between the factors and the variables should be linear), and homoscedasticity (the variances of the errors should be constant).

The Gaussian or normal distribution has several important properties and is widely used in statistics and natural sciences. It's significant because it is the distribution that maximizes entropy among all distributions with given mean and variance, making it the most "uninformative" and often serving as a good default choice in many scenarios. Also, according to the central limit theorem, the sum of many independent and identically distributed (i.i.d.) random variables tends toward a normal distribution.