AP Stats 1.4-1.8 Vocab Sheet

Categorical Variable

Places data into groups or categories.

Quantitative Variable

Numerical data

Discrete

Digits you count

Continuous

Can contain decimals

Distribution

The overall pattern of data.

Shape

The form of a distribution (symmetric, skewed left, skewed right).

Spread (Variability)

How much the data values differ from one another.

Mean, Median, Range

• Mean: The average of a data set.

• Median: The middle value when data is ordered.

• Range: Largest value minus smallest value.

Five-Number Summary

Minimum, Q1, Median, Q3, Maximum.

IQR (Interquartile Range)

The spread of the middle 50% of the data; Q3−Q1.

Standard Deviation (SD)

The typical distance of data values from the mean.

Resistant Statistic

Not greatly affected by outliers.

Non-Resistant Statistic

Greatly affected by outliers.

Percentile

The percentage of observations at or below a value.

Z-Score

The number of standard deviations a value is above or below the mean

Standardizing

Converting values into z-scores.

Boxplot

A graph showing the five-number summary.

Histogram

A graph displaying quantitative data using intervals.

Stemplot

• A graph that organizes data by place value while showing actual values.

Linear Transformation

Applying the same mathematical change to every value in a data set.

Bar Chart

categorical data

S = Shape

• Symmetric → mean ≈ median

• Skewed Right → mean > median

• Skewed Left → mean < median

Outlier Rule

Lower Fence:

Q1−1.5(IQR)

Upper Fence:

Q3+1.5(IQR)

Outlier if outside either boundary.

Comparing Quantitative Distributions

Use SOCS and compare in context.

Compare:

• Shape

• Outliers

• Center

• Spread

Example:

Team A has a higher median score than Team B.

Team A has less variability because its IQR is smaller.

Z-ScoresFormula:

z=x−meanSD

Meaning

• z > 0 → above mean

• z < 0 → below mean

• z = 0 → at mean

Interpretation

The value is ___ standard deviations above/below the mean.

Finding a Value from z

x=mean+z(SD)

Add/Subtract a Constant

Example:

y=x+5

Changes

• Mean: +5

• Median: +5

Stays Same

• Shape

• SD

• IQR

• Range

Memory:

Center changes, spread stays.

Multiply/Divide by a Constant

Example:

y=2x

Everything Multiplies by 2

• Mean

• Median

• SD

• IQR

• Range

Stays Same

• Shape

Memory:

Center and spread change.

Biggest Rules

• Right skew → mean > median

• Left skew → mean < median

• Median & IQR are resistant

• Mean & SD are non-resistant

• Positive z = above mean

• Negative z = below mean

• Add/Subtract → center changes, spread stays

• Multiply/Divide → center and spread change

• Standardized distributions: Mean = 0, SD = 1

• Describe distributions using SOCS