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.

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.

Inference in multiple linear regression primarily involves interpreting the coefficients of the model, which represent the expected change in the response variable for each one-unit change in the respective explanatory variable, assuming all other variables are held constant.

In a Chi-square test for goodness of fit, the degrees of freedom are calculated as the number of categories minus 1.

If events A and B are independent, the probability of both events occurring (P(A ∩ B)) is the product of their individual probabilities (P(A) * P(B)). This is a direct result of the Multiplication Rule for independent events.

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.

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.

The power of a test is influenced by the effect size - the magnitude of the difference or relationship you're testing for. Larger effect sizes increase the power of a test because they create a larger signal relative to the noise, making it easier to detect an effect if one exists.

The height of a bar in a histogram represents the frequency (or relative frequency) of data for that particular bin. This means the taller the bar, the more data falls into that specific interval.

Normalization or standardization ensures that all features contribute equally to the final distance calculation, regardless of their original scale. Without this step, features with larger scales would dominate the distance calculation, potentially leading to misleading clusters.