The main limitation of the mean as a measure of central tendency is that it is highly sensitive to outliers or extreme values. An outlier can skew the mean and make it a less accurate representation of the data. Moreover, mean does not describe the middle value or most common value in the dataset, which are often important characteristics.

A 95% confidence interval estimates the range within which we are 95% confident that the true population parameter lies. It is not about the range of the data or the mean of the sample.

Monotonic transformations do not affect the Spearman’s rank correlation coefficient. This is because Spearman's correlation is based on the rank order of data, and monotonic transformations preserve this order.

The main difference between a histogram and a bar plot is the type of data they represent. A histogram is used for continuous data, where the bins represent ranges of data, while a bar plot is used for categorical data to compare the frequency or count of different categories.

The error term in a simple linear regression model is the difference between the observed and predicted values. It captures the variability in the dependent variable that is not explained by the independent variable in the model.

If the residuals are not randomly distributed (e.g., if they form a pattern), it suggests that the linear regression model is not a good fit for the data. This could be because the relationship between the variables is not linear, or because the data exhibits heteroscedasticity (unequal variances of errors), among other reasons.

The Chi-square test for goodness of fit is used with categorical data. It compares the observed frequencies in each category with the frequencies we would expect to see if the data followed the theoretical distribution.

In the Mann-Whitney U test, the null hypothesis is that there is no significant difference between the groups. More specifically, it states that the probability that a randomly selected value from the first group is greater than a randomly selected value from the second group is equal to 0.5.

Increasing the sample size decreases the width of the confidence interval. The larger the sample size, the more information you have, and thus the less uncertainty (which translates into a smaller standard error and narrower confidence interval).

If A and B are independent events, the probability of both occurring is P(A ∩ B) which is equal to P(A) * P(B). This is the fundamental characteristic of independent events in probability.