Spearman's Rank Correlation is preferable to Pearson's correlation when the relationship between variables is non-linear but monotonic. Pearson's correlation measures linear relationships, while Spearman's can capture non-linear relationships.

The z-value associated with a 95% confidence interval in a standard normal distribution is approximately 1.96. This means that we are 95% confident that the true population parameter lies within 1.96 standard deviations of the sample mean.

The interquartile range, which is the difference between the upper quartile (Q3) and the lower quartile (Q1), represents the middle 50% of the data and is not affected by outliers. The range, on the other hand, is the difference between the maximum and minimum data values and is significantly affected by outliers.

Outliers can have a significant impact on the result of K-means clustering. They can distort the shape and size of the clusters, as they may pull the centroid towards them, creating less accurate and meaningful clusters.

A positive Pearson's Correlation Coefficient indicates a positive relationship between two variables. This means that as one variable increases, the other variable also increases, and vice versa.

The assumptions made in simple linear regression include linearity (the relationship between the independent and dependent variables is linear), homoscedasticity (the variance of the residuals is constant across all levels of the independent variable), and normality (the residuals are normally distributed).

The coefficient of variation (CV) is a standardized measure of dispersion that is unitless. It's particularly useful when comparing the dispersion of two or more datasets that have different units or significantly different means. Standard deviation, on the other hand, has the same units as the data, which may not be helpful for comparisons across different datasets.

The conditional probability of an event A given an event B equals the marginal probability of A when A and B are independent. This is because the occurrence of B does not change the probability of A if they are independent.

The Mann-Whitney U test is used for ordinal data, which can be ranked but have unknown or non-equivalent differences between values. It can also be used with interval and ratio data that do not meet the assumptions of other tests.

The mode in a data set refers to the most frequently occurring value. In a dataset, the mode is the value that appears the most number of times. A dataset may have one mode (unimodal), two modes (bimodal), or multiple modes (multimodal).