Statistics Terminology and Sampling Methods Quiz

Statistics vs. Parameters

• A sample is a subset of data collected from a population.
• A population is the entire set of data of interest.
• An element is an individual data point within a sample or population.
• A statistic is a numerical value that describes a sample, while a parameter is a numerical value that describes a population.
• Variable types include discrete (finite and countable) and continuous (infinite and measurable).

Sampling Methods

• Simple random sample (SRS): every element has an equal chance of being selected.
• Cluster sampling: dividing the population into smaller groups (clusters) and randomly selecting clusters.
• Stratified sampling: dividing the population into subgroups and sampling from each subgroup.
• Convenience sampling: selecting elements based on convenience and accessibility.

Descriptive Summaries for Data and Ways to Visualize Them

• Qualitative data: bar graph, pie chart
• Quantitative data: histogram, stem and leaf plot, dot plot, box plot
• Distribution shapes: left-skewed, right-skewed, symmetric, unimodal
• Formula for determining if a data point is a potential outlier: |xi - Q3| > 1.5*IQR

Measures of Central Tendency

• Mean: average value of a dataset; sensitive to outliers.
• Median: middle value of a dataset when in order; resistant to outliers.
• Mode: most frequent value in a dataset; resistant to outliers.
• Statistical symbols and formulas for sample and population means: x̄, μ

Measures of Variation

• Range: difference between the largest and smallest values.
• Variance/standard deviation: measures of spread or dispersion; formulas: s², σ², s, σ
• Interquartile range (IQR): difference between Q3 and Q1.
• Percentiles: percentage of values below a certain point.
• Statistical notation for sample and population variances/standard deviations: s², σ²

Probability

• Event: a set of outcomes of an experiment; simple event (one outcome) or compound event (multiple outcomes).
• Sample space: set of all possible outcomes of an experiment.
• Mutually exclusive events: cannot occur simultaneously.
• Independent events: occurrence of one does not affect the other.
• Addition Rule: P(A or B) = P(A) + P(B) - P(A and B)
• Complement Rule: P(A') = 1 - P(A)
• Intersection of events: P(A and B) = P(A) * P(B)

Discrete Random Variables

• Criteria for a discrete random variable to exist: countable and finite.
• Probability mass function (PMF): specifies the probability of each value of a discrete random variable.
• Cumulative distribution function (CDF): accumulates probabilities of a discrete random variable.
• Expected value of a general discrete random variable: E(X) = ∑xP(x)
• Variance/standard deviation of a general discrete random variable: Var(X) = E(X²) - [E(X)]²