K-means clustering requires the number of clusters to be defined beforehand, while hierarchical clustering does not. Hierarchical clustering forms a dendrogram from which the user can choose the number of clusters based on the problem requirements.

The sampling distribution in statistics is the probability distribution of a given statistic based on a random sample. For a statistic that is calculated from a sample, each different sample could (and likely will) provide a different value of that statistic. The sampling distribution shows us how those calculated statistics would be distributed.

Multicollinearity refers to a high correlation among independent variables in a regression model. It does not reduce the predictive power or reliability of the model as a whole, but it can cause instability in the estimation of individual regression coefficients, making them difficult to interpret.

The binomial distribution approaches the normal distribution as the number of trials gets large, provided that the probability of success is not too close to 0 or 1. This is known as the De Moivre–Laplace theorem.

Bar plots are commonly used in data analysis to compare the frequency, count, or proportion of categorical variables. Each category is represented by a separate bar, and the length or height of the bar represents its corresponding value.

Stratified random sampling differs from simple random sampling in that it first divides the population into non-overlapping groups, or strata, based on specific characteristics, and then selects a simple random sample from each stratum. This can ensure that each subgroup is adequately represented in the sample, which can increase the precision of estimates.

Homoscedasticity refers to the assumption that the residuals (errors) have constant variance at each level of the independent variable(s). This is important for the reliability of the regression model.

In an ANOVA test, the F-statistic is the ratio of the between-group variability to the within-group variability. In other words, it measures how much the means of each group vary between the groups, compared to how much they vary within each group. A larger F-statistic implies a greater degree of difference between the group means.

A negative kurtosis value indicates that the distribution has lighter tails and a flatter peak than the normal distribution. It means there are fewer outliers (extreme values), thus it is less outlier-prone than a normal distribution.

The primary assumption for a Z-test is that the population standard deviation is known. While a large sample size and normal distribution are often associated with Z-tests, they're not the primary assumption.

A histogram is a graphical representation of the distribution of a dataset. It is an estimate of the probability distribution of a continuous variable. To construct a histogram, the first step is to "bin" the range of values, i.e., divide the entire range of values into a series of intervals, and then count how many values fall into each interval.

In a normal distribution, the mean, median, and mode all coincide, meaning they have the same value. A normal distribution is symmetrical, with the majority of observations clustering around the central peak; therefore, the mean, median, and mode all fall at the center.