AP Statistics Module 1 Review

Variable

A characteristic that can be measured or categorized

Categorical Variable

Groups or labels (e.g., eye color)

Quantitative Variable

Numerical values that can be measured

Discrete Variable

Quantitative values that are countable (e.g., # of pets)

Continuous Variable

Quantitative values measured on a scale (e.g., height)

Distribution

The pattern of variation in data

Center

A typical value (mean, median, mode)

Spread

How much the data varies (range, IQR, standard deviation)

Shape

The form of the distribution (symmetric, skewed, uniform, bimodal)

Outlier

A data point far from the others, checked using the 1.5×IQR rule

Interquartile Range (IQR)

Middle 50% of data, Q3 – Q1

Percentile

The value below which a certain percent of observations fall

Z-score

Standardized value: how many standard deviations from the mean

Standard Deviation

Average distance of values from the mean

Variance

The square of the standard deviation

Normal Distribution

Symmetric, bell-shaped distribution

68–95–99.7 Rule

Rule describing proportions of data within 1, 2, and 3 standard deviations in a normal distribution

Boxplot aka Box and Whisker Plot

Graph showing the five-number summary (min, Q1, median, Q3, max)

Histogram

Graph for quantitative data using touching bars

Bar Chart

Graph for categorical data using separate bars

Dotplot

Graph showing each data point as a dot

Stemplot

Graph that preserves data values while showing distribution shape

What’s the difference between categorical and quantitative variables?

Categorical = groups/labels; Quantitative = numerical, measurable

What is the difference between discrete and continuous quantitative variables?

Discrete = countable (ex: # of pets); Continuous = measurable (ex: height)

What are the main ways to describe a distribution?

Shape, center, spread, and unusual features (SOCS)

What are the common measures of center?

Mean, median, and mode

What are the common measures of spread?

Range, IQR, and standard deviation

How do you calculate the interquartile range (IQR)?

Q3 – Q1

How do you check for outliers using the 1.5 × IQR rule?

If value < Q1 – 1.5 × IQR or > Q3 + 1.5×IQR

What does a percentile tell you?

The percentage of data values below a given value

What does a z-score measure?

How many standard deviations a value is from the mean

What is the formula for a z-score?

(x – μ) / σ

What are common graphs for categorical data?

Bar charts and pie charts

What are common graphs for quantitative data?

Histograms, dotplots, stemplots, and boxplots

What is the shape of a normal distribution?

Symmetric, bell-shaped, mean = median = mode

What is the 68–95–99.7 rule?

In a normal distribution: ~68% within 1σ, 95% within 2σ, 99.7% within 3σ