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Introductory Statistics Key Concepts

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Termini in questo insieme (41)

  • Population vs Sample

    Population is the entire group; Sample is a subset of the population.

  • Parameter vs Statistic

    Parameter describes a population; Statistic describes a sample.

  • Discrete vs Continuous Data

    Discrete data are counted (e.g., number of siblings); Continuous data are measured (e.g., height).

  • Levels of Measurement (N.O.I.R.)

    Nominal: categories without order; Ordinal: ordered categories; Interval: ordered with equal intervals, no true zero; Ratio: ordered with equal intervals and true zero.

  • Random Sampling

    Each member of the population has an equal chance of being selected.

  • Convenience Sampling

    Sampling individuals who are easiest to reach.

  • Voluntary Response Sampling

    Participants choose whether to participate, often leading to bias.

  • Systematic Sampling

    Select every kth individual from a list or sequence.

  • Cluster Sampling

    Randomly select entire groups or clusters from the population.

  • Stratified Sampling

    Divide population into groups and randomly sample from each group.

  • Biased Sample

    A sample that does not fairly represent the population, often due to poor sampling methods.

  • Lurking Variable

    A variable not included in the study that may affect the results.

  • Experiment vs Observation

    Experiment: applies treatment; Observation: no treatment applied.

  • Types of Studies (3)

    Cross-sectional: data at one time; Retrospective: looks back at past data; Prospective: follows subjects into the future.

  • Class Width

    Difference between lower limit of next class and current class.

  • Class Midpoint

    Calculated as (Lower class limit + Upper class limit) / 2.

  • Class Boundaries (example)

    For class 20–29, boundaries are 19.5–29.5 to avoid gaps between classes.

  • Relative Frequency

    Frequency divided by total frequency.

  • Cumulative Frequency

    Sum of frequencies up to a certain class as you move down the table.

  • Mean

    Sum of all data values divided by the number of values.

  • Median

    Middle value when data are ordered from least to greatest.

  • Mode

    Value that occurs most frequently in the data set.

  • Range

    Difference between maximum and minimum values.

  • Z-Score Interpretation

    z = 0: at mean; z > 0: above mean; z < 0: below mean.

  • Percentile

    The kth percentile means approximately k% of data are at or below that value.

  • Quartiles

    Q1: 25th percentile; Q2: 50th percentile (median); Q3: 75th percentile.

  • Interquartile Range (IQR)

    Difference between Q3 and Q1; represents the middle 50% of data.

  • Outlier Fences

    Lower fence = Q1 − 1.5(IQR); Upper fence = Q3 + 1.5(IQR).

  • Stem-and-Leaf Plot

    Stem: leading digit(s); Leaf: final digit of data values.

  • Box Plot Components

    Minimum, Q1, Median, Q3, Maximum values displayed graphically.

  • Dot Plot

    Each dot represents one observation; multiple dots stacked for repeated values.

  • Sample Mean Notation

    Sample mean is denoted by \(\bar{x}\).

  • Population Mean Notation

    Population mean is denoted by \(\mu\).

  • Mean Formula

    \(\bar{x} = \frac{\sum x}{n}\) where n is sample size.

  • Range Formula

    \(\text{Range} = \text{Max} - \text{Min}\)

  • Weighted Mean Formula

    \(\bar{x}_w = \frac{\sum wx}{\sum w}\) where w are weights.

  • Z-Score Formula

    \(z = \frac{x - \mu}{\sigma}\) measures how many standard deviations x is from the mean.

  • IQR Formula

    \(\text{IQR} = Q_3 - Q_1\)

  • Regression Equation

    \(\hat{y} = a + bx\) where a is y-intercept and b is slope.

  • Sample Standard Deviation Formula

    \(s = \sqrt{\frac{\sum (x - \bar{x})^2}{n-1}}\)

  • Population Standard Deviation Formula

    \(\sigma = \sqrt{\frac{\sum (x - \mu)^2}{N}}\)