In a skewed distribution, the mean tends to get pulled in the direction of the skew. Since the mean involves every value in the distribution, extreme values (values far from the others) have a big influence. This results in skewness where the mean is drawn towards the tail, and is a common occurrence in distributions that are not symmetric.

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, 68% of the data fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. This rule provides a quick estimate of the probability of a certain event within the distribution.

ANOVA stands for Analysis Of Variance. It's a statistical technique used to check if the means of two or more groups are significantly different from each other.

The Central Limit Theorem states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined (finite) expected value and finite variance, will be approximately normally distributed, regardless of the shape of the original distribution.

Polynomial regression models relationships as curves, not straight lines. This allows polynomial regression to capture non-linear relationships, where the relationship changes direction at different levels of the independent variables. On the other hand, linear regression models relationships as straight lines, assuming a constant rate of change.

Pearson's Correlation Coefficient assumes that the variables are normally distributed. It's one of the key assumptions made when calculating the coefficient, and it refers to the shape of the distribution of the values.

In factor analysis, eigenvalues represent the total variance explained by each factor. A larger eigenvalue indicates that more of the total variance is accounted for by that factor.

The Mann-Whitney U test is a non-parametric test, meaning it can be used when data can't be reasonably fit to a normal distribution.

The primary goal of statistics in data science is to provide a foundation for decision making based on data analysis. It is a discipline that provides tools and methods to interpret and understand data, answer specific questions, and visualize data in a meaningful way. This field of study is crucial in areas where constructing decisions are essential, such as business strategies, scientific research, policy making, etc.

The Central Limit Theorem (CLT) applies to the sampling distribution of the mean for a wide range of underlying distributions, provided the sample size is sufficiently large and the underlying distribution has finite variance.