Unit 3 Dispersion

These vocabulary flashcards cover the fundamental concepts, terms, and formulas related to measures of dispersion, their types, and associated statistics from Unit 3 (Dispersion) of BCOM304: Basics of Statistics & Mathematics.

Dispersion

The extent to which data values are scattered or clustered around a central value.

Measure of Dispersion

A statistical technique that quantifies the spread or variability of a dataset (e.g., range, variance, standard deviation).

Range

The simplest distance measure of dispersion calculated as the highest value minus the lowest value in a dataset (R = H – L).

Coefficient of Range

Relative measure of range given by (H – L)/(H + L); unit-free and useful for comparison.

Interquartile Range (IQR)

Distance between the third quartile (Q3) and the first quartile (Q1); represents the spread of the middle 50 % of data.

Quartile Deviation (QD)

Half of the interquartile range; also called the semi-interquartile range.

Coefficient of Quartile Deviation

Relative measure of QD, computed as (Q3 – Q1)/(Q3 + Q1).

Distance Measure

Category of dispersion measures based on differences between data points (e.g., range, IQR).

Average Deviation Measure

Category of dispersion measures that average the deviations of observations from a central value (e.g., MAD, variance).

Mean Absolute Deviation (MAD)

Average of the absolute differences between each data point and the mean (or median) of the dataset.

Coefficient of MAD

MAD divided by its central measure (mean or median); often expressed as a percentage.

Variance

Average of the squared deviations of observations from the arithmetic mean; symbolised as σ² for a population or s² for a sample.

Population Variance (σ²)

Variance computed using every value in the population; denominator equals N.

Sample Variance (s²)

Estimator of population variance based on a sample; denominator equals n – 1 to reduce bias.

Standard Deviation

Positive square root of the variance; retains the original units of the data and measures typical deviation from the mean.

Coefficient of Variation (CV)

Relative measure of dispersion calculated as (Standard Deviation / Mean) × 100 %; enables comparison across different units.

Combined Standard Deviation

Pooled standard deviation of two datasets, accounting for their individual means, standard deviations, and sizes.

Chebyshev’s Theorem

Rule stating that at least 1 – 1/z² of observations lie within z standard deviations of the mean for any distribution (z > 1).

Empirical Rule (68-95-99.7 Rule)

For a symmetric (normal) distribution: ≈68 % of data within 1 σ, 95 % within 2 σ, and 99.7 % within 3 σ of the mean.

Absolute Measure

Dispersion statistic expressed in the original units of data (e.g., Rs., cm); suitable for datasets with the same unit.

Relative Measure

Unit-free statistic expressed as a ratio or percentage; allows comparison across datasets with different scales.

Skewness

Measure of asymmetry in a distribution; indicates direction and degree to which data deviate from symmetry.

Measure of Skewness

Statistical method used to quantify the direction and extent of asymmetry in a dataset.

Symmetrical Distribution

Distribution in which mean, median, and mode coincide; data are evenly spread on both sides of the centre.

Positively Skewed Distribution

Distribution with a long right tail; mean is greater than median.

Central Tendency

Central value around which data cluster; commonly measured by mean, median, or mode.

Arithmetic Mean (x̄ or μ)

Sum of all observations divided by the number of observations; a measure of central tendency.

Median

Middle value of an ordered dataset; 50 % of observations lie on each side.

Mode

Most frequently occurring value in a dataset.

Partition Values

Measures (quartiles, deciles, percentiles) that divide ordered data into equal parts.

Quartiles (Q1, Q2, Q3)

Values that split an ordered dataset into four equal parts.

Deciles

Values that divide an ordered dataset into ten equal parts.

Percentiles

Values that divide an ordered dataset into one hundred equal parts.

Outlier

Observation markedly smaller or larger than the rest of the data; can distort dispersion measures like range.

Population

Entire group of objects or individuals under study.

Sample

Subset of the population selected for analysis; intended to represent the whole.

Sample Size (n)

Number of observations in a sample.

Population Parameter

Numerical summary calculated from the entire population (e.g., μ, σ).

Sample Statistic

Numerical summary calculated from sample data (e.g., x̄, s).

Cumulative Frequency

Running total of frequencies up to a given class or point in a dataset.