AP Stats Quiz Study

Categorical Data

Data that can be divided into groups or categories, often analyzed to determine if associations exist between variables.

Associated Variables

Two variables are considered associated when they are not independent of each other.

Independent Variables

Two variables are considered independent when they are not associated, meaning knowledge of one provides no information about the other.

CSOCS

An acronym for analyzing quantitative data including Context, Shape, Outliers, Center, and Spread.

Standard Deviation

A measure of the dispersion of a set of data points from its mean, indicating how spread out the numbers are.

Interquartile Range (IQR)

The difference between the third quartile (Q3) and the first quartile (Q1), used to measure the spread of the middle 50% of data.

Boxplot

A graphical display of the five-number summary of a data set, showing outliers and the distribution of the data.

Stemplot

A method for displaying quantitative data by splitting data points into 'stems' and 'leaves'.

Lower Fence

Calculated as Q1 - 1.5 times the IQR, used to identify potential outliers.

Upper Fence

Calculated as Q3 + 1.5 times the IQR, used to identify potential outliers.

Outliers

Data points that fall outside the lower and upper fences, which may indicate unusual occurrences in the data set.

Context in CSOCS

In quantitative analysis, context refers to the background information necessary to understand the data, including units of measurement.

Shape in CSOCS

The general distribution pattern of the data, which can be normal, skewed, or bimodal.

Center in CSOCS

The central tendency of data represented usually by the mean or median.

Spread in CSOCS

The variability of the data which can be measured using range or IQR.

Associated Variables

Two categorical variables are associated (not independent) if the percentage distribution of one variable differs across categories of the other, meaning at least two probabilities are unequal.

Independent Variables

Two categorical variables are independent (not associated) if the percentage distribution of one variable remains identical across all categories of the other variable.

CSOCS

A strategy for describing quantitative distributions: Context (including units), Shape (skewed, symmetric, unimodal, bimodal), Outliers (and gaps), Center (mean or median), and Spread (range or IQR).

First Quartile ($Q_1$)

The median of the lower half of an ordered data set.

Third Quartile ($Q_3$)

The median of the upper half of an ordered data set.

Interquartile Range ($IQR$)

The measure of spread calculated as $IQR = Q<em>3 - Q</em>1$.

Outlier Fences

Boundaries used to identify outliers: Lower Fence = $Q<em>1 - 1.5 \times IQR$; Upper Fence = $Q</em>3 + 1.5 \times IQR$.

Standard Deviation ($s$)

A measure of how spread out the values in a distribution are from the mean. A low value means data cluster near the mean; a high value indicates greater spread.

Sample Variance ($s^2$)

The sum of squared deviations from the mean divided by $n - 1$.

Standard Deviation Interpretation

"On average, a randomly-selected [context] will be [SD units] away from the mean of [mean units]."

Boxplot Whiskers

Lines drawn from the box ($Q<em>1$ and $Q</em>3$) extending to the most extreme non-outlier data points within the fences, rather than to the fences themselves.

Stemplot Structure

A quantitative display where each value is split into a stem (all leading digits to the left) and a leaf (the single final digit on the right).