AP®︎ Statistics: Topic 1.9 Flashcards

Examining how the same quantitative variable differs across groups, samples, populations, times, or conditions by explicitly comparing shape, center, variability, and unusual features

The variable being compared must be the same measurement with the same units in all distributions

Compare distributions by shape, center, variability, and unusual features such as outliers, gaps, and clusters

A comparison must name the variable, identify the groups, and include units when given

Skew is named for the longer tail: long tail to larger values means skewed right, long tail to smaller values means skewed left

Use median with IQR for skewed distributions or distributions with outliers because both measures are resistant

Use mean with standard deviation for approximately symmetric distributions without strong outliers because both are nonresistant

Median and IQR are resistant to extreme values; mean, standard deviation, and range are nonresistant

In symmetric distributions mean and median are close; in right-skewed mean > median; in left-skewed mean < median

Maximum minus minimum; describes the full observed span and is strongly affected by extreme values

Q3 - Q1; measures the spread of the middle 50% of the data and is resistant to outliers

A typical distance of observations from their mean; a nonresistant measure of spread

An observation is a potential outlier if it is below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR)

An interval with no observed values

A concentration of observations, often separated from another concentration by a gap

Histograms for multiple groups compared on aligned axes using the same bin boundaries and bin widths

A histogram showing proportions instead of counts; often better than frequency histograms when group sizes differ

Comparative dotplots on a common quantitative scale that retain every observed value

A stem-and-leaf plot with common stems in the center and leaves for two groups on opposite sides using the same stem and leaf units

The key states what a stem and leaf represent, which is necessary because the same digits could mean different scales

Boxplots for two or more groups on a common quantitative scale used to compare medians, IQRs, overall ranges or nonoutlying ranges, potential outliers, and possible skewness

Boxplots show medians, IQRs, ranges, outliers, and possible skewness, but not mean, standard deviation, detailed modality, gaps, or clusters

A boxplot that marks potential outliers separately and extends whiskers only to the most extreme nonoutlying values

Comparative graphs must use compatible scales, and comparative histograms must use the same bin boundaries and widths, or visual comparisons may be misleading

Shared values between distributions; a higher center for one group does not mean every observation in that group is higher

Histograms usually allow only approximate conclusions about center, spread, or outliers because individual exact values are grouped into bins

A measure of relative position that tells how many standard deviations a value is above or below the mean; the standardized score most commonly used is the z-score

z = (x - μ) / σ

When population parameters are unknown, z may be computed as (x - x̄) / s

Positive z means above the mean, negative z means below the mean, and z = 0 means equal to the mean

A z-score is unitless because both x - μ and σ are measured in the same units

Converting values to z-scores preserves order and shape but changes the center to 0 and the standard deviation to 1

Where a value falls within its own distribution, judged relative to that distribution’s mean and spread rather than by raw value alone

The larger signed z-score is the higher relative position within its distribution

|z| measures distance from the mean without regard to direction; larger |z| means more extreme relative to the mean

A z-score alone does not give a percentile or probability without additional information about the distribution’s model or shape

An outlier is unusual relative to its own distribution, not just because it is larger or smaller than values in another group