Unit 1 Review: Advanced Distribution Analysis

SOCS

An acronym for Shape, Outliers, Center, and Spread, used to describe and compare distributions.

Shape

The visual appearance of the distribution—symmetric, skewed right, skewed left, or uniform.

Outliers

Data points that deviate significantly from other observations, often identified using the 1.5 x IQR rule.

Center

The measure of the central tendency of a distribution, such as mean or median.

Spread

A measure of the variability of a dataset, often described using standard deviation or interquartile range (IQR).

Comparative Language

Language that explicitly compares statistics and uses linking words to show relationships between groups.

Mean

The average of a set of values, calculated by dividing the sum of the values by the number of values.

Median

The middle value of a dataset when arranged in ascending order, serving as a measure of center.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

Interquartile Range (IQR)

The range between the first quartile (Q1) and the third quartile (Q3), representing the middle 50% of the data.

Normal Distribution

A continuous probability distribution that is symmetric and bell-shaped, fully defined by its mean and standard deviation.

Empirical Rule

A rule that states that for a normal distribution, approximately 68% of values fall within 1 standard deviation of the mean, 95% fall within 2, and 99.7% fall within 3.

z-Score

A statistical measurement that describes a value's relation to the mean of a group of values in terms of standard deviations.

Percentile

A value below which a percentage of observations in a group falls.

Standard Normal Distribution

A normal distribution with a mean of 0 and a standard deviation of 1, denoted as N(0, 1).

Resistance

The property of a statistic that is not significantly affected by extreme values; the median and IQR are resistant.

Non-resistance

The property of a statistic that is significantly affected by extreme values; the mean and standard deviation are non-resistant.

Unimodal

Having one mode; typically refers to a distribution with a single peak.

Bimodal

Having two modes; typically refers to a distribution with two distinct peaks.

Skewed Right

A distribution where the tail on the right side is longer or fatter than the left side; mean > median.

Skewed Left

A distribution where the tail on the left side is longer or fatter than the right side; mean < median.

Gaps in Data

Spaces in the data distribution where no observations occur, which may indicate unusual features.

Graphical Representations

Visual methods used to display data distributions, such as boxplots, stemplots, and histograms.

Two-Variable Data

Data that involves two variables, allowing for comparisons between distributions.

Normal Curve Characteristics

Features of the normal distribution: symmetric, unimodal, and bell-shaped.

CUSS

An alternate mnemonic for the comparison framework: Center, Unusual features (Outliers), Shape, Spread.