chapter one (all)

Density Curve

A density curve is a curve that is always on or above the horizontal axis and has an area of exactly 1 underneath it.

Median of a Density Curve

The median of a density curve is the equal-areas point that divides the area under the curve in half.

Mean of a Density Curve

The mean of a density curve is the balance point, where the curve would balance if made of solid material.

Normal Distribution

A distribution with a bell-shaped density curve, parameterized by mean (μ) and standard deviation (σ).

Empirical Rule

Approximately 68% of observations fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Z-Score

A standardized value calculated as z = (x - μ) / σ, representing how many standard deviations an observation is from the mean.

Standard Normal Distribution

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

Area Under the Normal Curve

Represents proportions (probabilities) of observations from the normal distribution.

TI-83TM Calculator

A calculator used to compute areas under the normal curve; commands include normalcdf for finding areas.

Cumulative Proportion

The area under the curve to the left of a number x, representing the proportion of observations below that value.

Inverse Normal Calculations

Finding a value x corresponding to a given area proportion under the normal curve using the equation: x = μ + σz.

Statistic

A numerical summary of data.

Mean

The average value of a dataset, calculated by summing all observations and dividing by the number of observations.

Median

The midpoint of a distribution, where half of the observations are smaller and half are larger.

Quartiles

Values that divide a dataset into four equal parts; includes Q1 (25th percentile), Q2 (50th percentile; median), and Q3 (75th percentile).

Interquartile Range (IQR)

The distance between the first (Q1) and third quartile (Q3), IQR = Q3 - Q1.

Outlier

An observation that falls more than 1.5 times the IQR above the third quartile or below the first quartile.

Five-Number Summary

A summary of a dataset that includes the minimum, Q1, median (M), Q3, and maximum.

Standard Deviation

A measure of the spread or dispersion of a set of observations, indicating how much the values deviate from the mean.

Variance

The average of the squared differences from the mean, representing the spread of data points.

Robust Statistic

A statistic that is not greatly influenced by outliers or small changes in the dataset.

Exploratory Data Analysis (EDA)

The application of one or more visual tools to help examine data and their main features.

Distribution of a categorical variable

Lists the categories and gives either the count or percent of individuals in each category.

Bar chart

A visual representation used to depict the distribution of a categorical variable.

Dot chart

A graphical display for comparing different categories by representing data points with dots.

Stemplot

A method used to visualize the shape of a distribution for a quantitative variable while including actual numerical values.

Back-to-back stemplot

A stemplot used to compare two related distributions using common stems.

Histogram

A graphical representation that visualizes the shape of a distribution for a quantitative variable by breaking the range into classes.

Mode

A major peak of a distribution; the distribution is unimodal, bimodal, or multimodal based on the number of peaks.

Outlier

An individual value that falls outside the overall pattern of a distribution.

Symmetric distribution

A distribution where values smaller and larger than its midpoint are mirror images of each other.

Skewed distribution

A distribution with an asymmetric shape where one tail is longer than the other.

Statistics

The science of learning from data.

Data

Numerical facts used to describe cases.

Variable

Any characteristic of an individual that can take different values.

Individual/Cases

The objects described by a set of data, which can be people, animals, or objects.

Context

The circumstances or details surrounding the data that are needed to understand its meaning.

Categorical Variable

A variable that places an individual into one of several groups.

Quantitative Variable

A variable that takes numerical values where arithmetic operations make sense.

Distribution of a Variable

Describes what values a variable takes and how often these values occur.

Unit of Measurement

The specific quantity used to measure a variable, necessary for its interpretation.