Statistics CH2 - Exploring data with graphs and numerical summaries.

Variable

A characteristic observed in a study; the characteristics observed vary

Quantitative Variable

Observations take numerical values representing different magnitudes of the variable

Categorical Variable

Observations belong to one of a set of categories

Observations

Data values observed for a variable; can be numerical or categorical

Center

The typical or middle value of a quantitative variable’s data

Variability (or Spread)

The extent to which data values vary or spread out

Discrete Quantitative Variable

Possible values form a set of separate numbers with a finite number of possible values

Continuous Quantitative Variable

Possible values form an interval; infinite continuum of possible values

Frequency Table

A listing of possible values of a variable with counts (frequencies) of observations for each value

Modal Category

The category with the highest frequency in categorical data

Mode

The numerical value with the highest frequency in quantitative data

Proportion

The frequency of observations in a category divided by the total number of observations

Percentage

Proportion multiplied by 100

Relative Frequencies

Proportions or percentages that sum to 100 (or 1)

Pie Chart

A circular graph displaying categories as slices proportional to their percentage of observations

Bar Graph

A graph with vertical bars showing percentages of observations in categories; bars separated in categorical data

Pareto Chart

A bar graph ordered from tallest to shortest bars, highlighting most common outcomes

Dot Plot

A graph showing individual data points just above a number line

Stem-and-Leaf Plot

A graph representing data values by stems and leaves showing individual observations and data order

Histogram

A graph using bars to show the frequency distribution of a quantitative variable; bars adjacent for continuous data

Overall Pattern

Whether data is clustered or contains gaps in its distribution

Gap

An interval in the data distribution where there are no observations

Unimodal

Distribution with a single mound (peak) in its data

Bimodal

Distribution with two distinct mounds (peaks)

Shape

The overall form of a data distribution; can be symmetric or skewed

Symmetric

Distribution where data is evenly distributed around the center

Skewed

Distribution where data has a tail; skewed right has a longer right tail; skewed left has a longer left tail

Tails

The lower parts (extremes) of a distribution

Time Series

Data collected over time

Time Plot

A graph displaying time series data with time on horizontal axis and observations on vertical axis

Trend

A general direction or pattern observed in data over time

Mean (Average)

Sum of data values divided by number of values; balance point of data

Median

Middle data value when values are ordered; resistant to outliers

Outliers

Data points unusually far from other observations

Resistant

Not greatly affected by extreme values or outliers

Variance

Average of squared deviations from the mean; measure of data variability

Standard Deviation

Square root of variance; typical distance of data points from the mean

Sum of Squares

Sum of squared deviations from the mean; basis for variance calculation

Empirical Rule

Rule describing percentage of data within 1, 2, and 3 standard deviations in bell-shaped distributions

Quartiles

Values dividing ordered data into quarters; Q1, Q2 (median), Q3

Percentiles

Values indicating the percent of data below that point

Interquartile Range (IQR)

Range between first and third quartiles; measure of middle 50% variability, resistant to outliers

Potential Outliers

Observations falling more than 1.5 times IQR below Q1 or above Q3

Five-number Summary

Minimum, Q1, median, Q3, and maximum; summarized by box plot

Box Plot

Graph displaying the five-number summary with a box and whiskers; identifies outliers

Whiskers

Lines extending from a box plot showing data range excluding outliers

Z-score

Number of standard deviations an observation is from the mean; measures position and potential outliers