DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering method that can find arbitrary shaped clusters and is less affected by outliers. It works based on the density of points in a region, growing clusters according to the density estimate.

The standard deviation measures 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 (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The skewness of a distribution can be determined using a box plot by looking at the position of the median in the box. If the median is not in the center of the box (i.e., the quartiles are not equidistant from the median), the data is skewed. If the median is closer to the bottom of the box, the data is positively skewed, and if it's closer to the top, the data is negatively skewed.

The Law of Large Numbers states that as a sample size grows, its mean gets closer to the average of the whole population. In other words, as the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.

If the p-value from a Mann-Whitney U test is less than the significance level (often 0.05), you would reject the null hypothesis, suggesting there is a significant difference between the groups.

A Residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.

The Mann-Whitney U test does not provide information about the shape of the distributions. It is a non-parametric test that does not make any assumptions about the distribution of the data.

Multiple linear regression analysis is used to understand the relationship between several independent (explanatory) variables and a dependent (response) variable. It can also be used for predicting the mean value of the dependent variable given the values of the independent variables.

The eigenvalue of a component in PCA is directly proportional to the variance of that component. In other words, a larger eigenvalue corresponds to a larger amount of variance explained by that principal component.

Simple random sampling is a basic type of sampling method where each individual in the population has an equal chance of being selected. This ensures that the sample will be representative of the population, making it easier to make accurate inferences about the whole population.