STAT 1220 - Test 1 Review Vocabulary

Vocabulary flashcards covering key statistics concepts from the lecture notes (population vs. sample, measures of center and spread, distributions, probability rules, and basic probability concepts).

Population

The entire group of individuals or elements of interest in a study.

Sample

A subset of the population chosen for study.

Parameter

A numerical characteristic of the population (often unknown).

Statistic

A numerical characteristic computed from a sample.

Mean

The arithmetic average of a data set; sum of values divided by the number of values.

Median

The middle value when data are ordered; for even n, the average of the two middle values.

Mode

The most frequently occurring value in a data set.

Standard Deviation (Sample)

A measure of spread for a sample: s = sqrt[(1/(n-1)) Σ (xi − x̄)²].

Variance (Sample)

The square of the sample standard deviation: s².

Z-score

The number of standard deviations a value lies from the mean: z = (x − x̄)/s.

Percentile Rank

The percentage of observations that are less than or equal to a given value.

Five-Number Summary

Minimum, Q1, median, Q3, maximum of a data set.

Interquartile Range (IQR)

Q3 − Q1; the spread of the middle 50% of the data.

Box Plot

A graphical display of the five-number summary showing quartiles and median.

Stem-and-Leaf Plot

A data display that shows distribution while preserving the actual values.

Normal Distribution (Bell-shaped)

A symmetric distribution determined by mean and standard deviation.

Empirical Rule (68-95-99.7)

In a normal distribution: ~68% within 1 sd, ~95% within 2 sd, ~99.7% within 3 sd.

Chebyshev's Inequality

For any distribution, at least 1 − 1/k² of data lie within k standard deviations of the mean.

Probability

A measure of how likely an event is, ranging from 0 to 1.

Complement Rule

P(Aᶜ) = 1 − P(A); the probability of the opposite of A.

Joint Probability

P(A ∩ B); the probability that both events occur.

Conditional Probability

P(A|B) = P(A ∩ B) / P(B); probability of A given B occurs.

Independence

Two events A and B are independent if P(A ∩ B) = P(A)P(B).

Union

P(A ∪ B); the probability that A or B (or both) occur.

Intersection

P(A ∩ B); the probability that both A and B occur.

Sample Space

The set of all possible outcomes of a random experiment.

Random Experiment

A process that yields outcomes with unpredictable results but well-defined probabilities.

Proportion

A part of the population with a given attribute, expressed as a fraction or percentage.

Binomial Distribution

Distribution of the number of successes in n independent Bernoulli trials with the same probability p.