Unit 1: Exploring One-Variable Data - Summary Statistics

Mean

The arithmetic average of a distribution, calculated by summing all observations and dividing by the number of observations.

Median

The value that divides a distribution into two equal halves, with half the observations falling below it and half above.

IQR (Interquartile Range)

The range of the middle 50% of the data, calculated as Q3 - Q1, and is resistant to outliers.

Outlier

A data point that differs significantly from other observations, typically falling outside the lower and upper fences determined by the 1.5 IQR rule.

Sample Mean

Denoted as ( \bar{x} ), it represents the average of a sample set.

Population Mean

Denoted as ( \mu ), it represents the average of the entire population.

Range

A basic measure of spread calculated as the difference between the maximum and minimum values in a dataset.

Standard Deviation

A measure of the typical distance of values from the mean, indicating how spread out the data points are.

Variance

The average of the squared differences from the mean, used to quantify variability in a dataset.

Robustness

The quality of a statistical measure to remain relatively unaffected by extreme values or outliers.

Resistant Measure

A statistical measure, such as the median, that is not significantly affected by outliers.

Non-Resistant Measure

A statistical measure, such as the mean, that is sensitive to outliers.

Five-Number Summary

A summary of a dataset consisting of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

Boxplot

A graphical representation of the five-number summary, illustrating the distribution of data and identifying outliers.

Skewed Right

A distribution where the tail on the right side is longer, typically resulting in ( Mean > Median ).

Skewed Left

A distribution where the tail on the left side is longer, typically resulting in ( Mean < Median ).

Degrees of Freedom

Refers to the number of values in a calculation that are free to vary, affecting the calculation of sample variance.

Q1 (First Quartile)

The median of the lower half of a dataset, dividing the lowest 25% of data from the rest.

Q3 (Third Quartile)

The median of the upper half of a dataset, dividing the highest 25% of data from the rest.

Min

The smallest observation in a dataset.

Max

The largest observation in a dataset.

Fences

Rules used to determine outliers via the 1.5 IQR method, consisting of lower and upper fences.

Comparative Language

Descriptive language used to compare two distributions, highlighting their differences in measures or characteristics.

S vs. P

Statistics come from samples (e.g., ( \bar{x}, s )), while parameters come from populations (e.g., ( \mu, \sigma )).

CUSS and BS

A mnemonic to remember what to describe when comparing distributions: Center, Unusual features, Shape, Spread, Be Specific.

Symmetric Distribution

A distribution where the mean and median are approximately equal, indicated by a balanced shape.