Math: Statistics Fundamentals

What is the median of a dataset?

The median is the exact middle value of a dataset when all the numbers are ordered from least to greatest.

How is the mean of a dataset calculated?

The mean is calculated by summing all the values in a dataset and dividing that sum by the total number of values.

Which measure of center is most affected by extreme outliers?

The mean is the measure of center most affected by extreme outliers because it incorporates every single value in its calculation.

What does the range of a dataset represent?

The range represents the total spread of a dataset, calculated as the difference between the highest and lowest values.

What is the mathematical relationship between variance and standard deviation?

The standard deviation is exactly the square root of the variance.

Why do we divide by (n-1) instead of n when calculating sample variance?

Dividing by (n-1), known as Bessel's correction, corrects the bias in the estimation of the population variance from a smaller sample.

What defines two independent events in probability?

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.

What is the formula for conditional probability, P(A|B)?

The conditional probability P(A|B) is calculated as the probability of A and B occurring together, divided by the probability of B: P(A and B) / P(B).

If two events are mutually exclusive, what is the probability of both occurring at the same time?

If two events are mutually exclusive, the probability of both occurring simultaneously is exactly zero.

What does the 68-95-99.7 (Empirical) rule state about a normal distribution?

The Empirical rule states that approximately 68%, 95%, and 99.7% of data fall within one, two, and three standard deviations of the mean, respectively.