Intro to Statistics - VOCABULARY Flashcards (Based on Lecture Notes)

Vocabulary-style flashcards covering core concepts, definitions, and key formulas from the lecture notes on Intro to Statistics.

Population

The entire group of interest in a study; the total set from which data could be drawn.

Sample

A subset of the population used to estimate population parameters.

Parameter

A true numerical value describing a population (often unknown, e.g., population mean μ or population proportion π).

Statistic

A numerical value calculated from a sample used to estimate a population parameter (e.g., x̄, p̂).

Population vs Sample (contrast)

Population is the whole group; sample is the part you actually measure.

Parameter vs Statistic (contrast)

Parameter describes the population; statistic describes the sample.

Categorical (Qualitative)

Variables that take distinct categories or labels (e.g., major, color, yes/no).

Quantitative (Numerical)

Variables that take numeric values (e.g., height, age, test scores).

Discrete

Quantitative variable that is countable (e.g., number of siblings).

Continuous

Quantitative variable that is measurable over a range (e.g., height, weight).

Bar Graph

A graph appropriate for categorical data showing counts or proportions.

Pie Chart

A circular chart showing proportions of a whole for categorical data.

Histogram

A graph for quantitative data showing the distribution (spread) of values.

Boxplot

A graph showing median, quartiles, and outliers to illustrate spread.

Mean

The average of a set of numbers (sum of values divided by n).

Median

The middle value when data are ordered.

Mode

The most frequent value in a data set.

Range

Difference between the maximum and minimum values (max − min).

IQR (Interquartile Range)

Difference between the 75th and 25th percentiles (Q3 − Q1).

Standard Deviation (s)

A measure of how spread out the data are around the mean (sample standard deviation).

Probability

The long-run proportion of times an event occurs; a value between 0 and 1.

Addition Rule

P(A or B) = P(A) + P(B) − P(A and B).

Multiplication Rule (independent)

If A and B are independent, P(A and B) = P(A) × P(B).

Complement Rule

P(A′) = 1 − P(A); used for 'not A' outcomes.

Random Variable

A variable that assigns a numerical value to each outcome of a random process.

Binomial Distribution

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

Binomial Mean

Mean μ = n × p.

Binomial SD

Standard deviation σ = sqrt(n × p × (1 − p)).

H0 (Null Hypothesis)

The default claim tested; often no effect or no difference (e.g., π = π0).

Ha (Alternative Hypothesis)

The claim being tested for (e.g., π > π0, π < π0, or π ≠ π0).

P-value

Probability, under H0, of obtaining a result as extreme or more extreme than observed.

One-sided Test

Tests for an effect in a specific direction (e.g., > or <).

Two-sided Test

Tests for any difference in either direction (≠).

p̂ (Sample Proportion)

x̂ = number of successes in the sample divided by n (x̂ = x/n).

π (Population Proportion)

True proportion in the population.

π0 (Null Proportion)

Proportion assumed under H0.

Proportion of a Characteristic

p̂ = x/n; used to summarize binary/categorical outcomes.

P(at least one)

Complement rule: P(at least one) = 1 − P(none).

Percent ↔ Decimal Conversions

Decimal to percent: multiply by 100; percent to decimal: divide by 100.

x% of N

Formula: (x/100) × N; used to compute portions of a total.

Rounding to 4 Significant Digits

Keep the first four significant figures; round up if the next digit is 5 or more.

Leading 0 before Decimal

Always include a 0 before the decimal point (e.g., 0.12, not .12).

Skew Direction

Right-skew: tail to the right; Left-skew: tail to the left.

Sensitivity

Probability of a positive test given the disease is present.

Specificity

Probability of a negative test given no disease is present.

Symbols You’ll See

n: sample size; N: population size; x̄: sample mean; μ: population mean; s: sample SD; σ: population SD; p̂: sample proportion; π: population proportion; π0: null proportion.

Graphs by Data Type

Pie/bar for categorical data; histogram/boxplot for quantitative data; bar charts should start y-axis at 0.