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Statistics for Business - Key Concepts and Methods

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이 집합의 용어 (43)

  • Operational Definition
    Specifies the type of variable and the measurement scale used for each variable identified in a business problem.
  • Numerical vs. Categorical Variables
    Numerical: data represent counted/measured quantities (discrete or continuous). Categorical: data represent categories or labels without inherent numeric meaning.
  • Discrete Numerical Variable
    Data arising from a counting process, representing a number of something (e.g., number of smartphones sold).
  • Continuous Numerical Variable
    Data arising from a measuring process, can take any value within an interval, limited by measurement precision (e.g., waiting time).
  • Measurement Scales for Numerical Variables
    Interval scale: differences meaningful, no true zero. Ratio scale: ordered scale with a true zero point indicating absence of the variable.
  • Measurement Scales for Categorical Variables
    Nominal scale: categories with no order. Ordinal scale: categories with a meaningful order but unequal intervals.
  • Population vs. Sample
    Population: entire group of interest. Sample: subset of the population used to estimate characteristics.
  • Statistic vs. Parameter
    Statistic: summary measure from a sample. Parameter: summary measure from a population.
  • Primary vs. Secondary Data Sources
    Primary: data collected directly by the analyst. Secondary: data collected by others and used by the analyst.
  • Observational Study vs. Designed Experiment
    Observational study: researcher observes without control. Designed experiment: researcher assigns treatments and controls conditions.
  • Frame in Sampling
    A complete or partial listing of the population items from which a sample is drawn; critical to avoid bias.
  • Nonprobability vs. Probability Sampling
    Nonprobability: selection without known probabilities; Probability: selection based on known probabilities allowing valid inference.
  • Simple Random Sampling (SRS)
    Every item has equal chance of selection; every sample of size n equally likely; foundation for other sampling methods.
  • Systematic Sampling
    Select every kth item from an ordered frame after a random start; faster but risks bias if hidden patterns align with k.
  • Stratified Sampling
    Divide population into strata by shared characteristic, then sample randomly within each stratum; improves precision and representation.
  • Cluster Sampling
    Divide population into clusters, randomly select clusters, and study all items within selected clusters; cost-effective for widespread populations.
  • Invalid Variable Values
    Values that violate operational definitions and cannot be reasonably corrected; must be flagged or removed.
  • Coding Errors
    Errors from data entry or processing that can often be corrected without external info (e.g., 'Female' instead of 'F').
  • Missing Values
    Data values that were never collected or are absent; distinct from miscoded values.
  • Outliers
    Numerical values excessively different from others; require review as they may affect statistical results.
  • Mean (Sample Mean)
    Sum of all values divided by number of values; sensitive to outliers.
  • Median
    Middle value in ordered data; resistant to outliers.
  • Mode
    Most frequently occurring value; data can be unimodal, multimodal, or have no mode.
  • Range
    Difference between largest and smallest values; simple but ignores distribution shape.
  • Variance and Standard Deviation
    Measure spread by averaging squared deviations from the mean; SD is square root of variance and in original units.
  • Coefficient of Variation (CV)
    Relative measure of variation expressed as a percentage; useful for comparing variability across different units.
  • Z-Score
    Number of standard deviations a value is from the mean; used to identify outliers.
  • Skewness
    Measure of asymmetry: negative (left-skewed), zero (symmetric), positive (right-skewed).
  • Kurtosis
    Measure of peakedness: leptokurtic (sharp peak, fat tails), platykurtic (flat peak).
  • Quartiles and Interquartile Range (IQR)
    Quartiles split data into four parts; IQR = Q3 − Q1 measures spread of middle 50%, resistant to outliers.
  • Boxplot
    Graphical summary showing median, quartiles, and potential outliers; visualizes distribution shape.
  • Probability
    Numerical measure of likelihood of an event, ranging from 0 (impossible) to 1 (certain).
  • Conditional Probability
    Probability of event A given event B has occurred: P(A|B) = P(A and B) / P(B).
  • Independence of Events
    Events A and B are independent if P(A|B) = P(A); occurrence of one does not affect the other.
  • General Addition Rule
    P(A or B) = P(A) + P(B) − P(A and B); accounts for overlap in events.
  • Multiplication Rule
    P(A and B) = P(A|B) × P(B); for independent events, P(A and B) = P(A) × P(B).
  • Binomial Distribution
    Models number of successes in n independent trials with constant success probability π; outcomes are discrete.
  • Poisson Distribution
    Models count of events in fixed interval with known average rate λ; events occur independently.
  • Normal Distribution
    Continuous, symmetric, bell-shaped distribution defined by mean μ and standard deviation σ.
  • Z-Transformation for Normal Distribution
    Converts X to standard normal Z: Z = (X − μ) / σ; used to find probabilities and critical values.
  • Empirical Rule
    In normal distribution, ~68% within ±1σ, ~95% within ±2σ, ~99.7% within ±3σ of mean.
  • Evaluating Normality
    Compare mean and median, check IQR/SD ratio, use histograms/boxplots, and construct normal probability plots.
  • Ethical Issues in Statistics
    Include selective reporting, misleading visuals, ignoring sampling methods, and misrepresenting probabilities.