AP Statistics Study Cards: Chapter 1 (Exploring Data)

Outlier

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

Overall Pattern (of a Distribution)

Shape, center, spread, and presence/absence of outliers describe the overall pattern of the distribution of a quantitative variable. (If there is a gap in the distribution, mention that also.)

Pie Chart

Used for showing the distribution of a categorical variable; must include all the categories that make up the whole.

Segmented Bar Graph

Used to compare the distribution of a categorical variable in multiple groups. The height of each segment within each bar is determined by the percent of individuals in the group with that value. Each bar has a total height of 100%.

Bar Graph

Used to display the distribution of a categorical variable; drawn with blank spaces between the bars to separate the items being compared.

Five-Number Summary

Used to make a boxplot; consists of the MINIMUM, Q1, MEDIAN, Q3, and the MAXIMUM.

Skewness

A distribution of a quantitative variable is skewed to the right (positively) if the right half of the graph is longer than the left half. It is skewed to the left (negatively) if the the left half is longer than the right half.

Symmetric

A distribution of quantitative data is symmetric if the upper and lower halves are approximate mirror images of each other.

Stemplot (or Stem and Leaf Plot)

A graph for fairly small quantitative data sets that gives a quick picture of a distribution's shape while including the specific values.

Bimodal

A graph of quantitative data with two clear peaks. (Note: unimodal implies one peak, multi-modal implies more than two peaks.)

Median

A measure of center in a set of quantitative data. The median of a list of values is the value appearing at the center of a sorted version of the list - or the mean of the two central values if the list contains an even number of values. Denoted M.

Standard Deviation

A measure of spread (variability) that describes the average distance of the observations from their mean.

Splitting Stems

A method for spreading out a stemplot that has too few stems.

Boxplot

A method of graphing quantitative data. The box spans the 1st and 3rd quartiles, showing the spread of middle 50% of the distribution. The median is marked within the box. Lines extend from the box to the highest and lowest values not considered outliers. Outliers show as isolated points.

Dotplot

A simple graph that shows each data value as a dot above its location on a number line.

Range

A single number computed by taking the difference: Maximum - Minimum. It is a measure of spread.

Interquartile Range (IQR)

A single number computed by taking the difference: Q3 - Q1. It is a measure of spread.

Resistant Measure

A statistic that is not greatly affected by extreme observations. (Non-resistant measures ARE greatly affected by extreme observations.) resistant: Median, IQR non-resistant: Mean, Standard Deviation, Range

Marginal Distribution

A two-way table has two marginal distributions. Each one is the distribution of values of one of the variables among all of the individuals described by the table.

Categorical Variable

A variable that names categories. (A categorical variable cannot be measured or counted.)

Quantitative Variable

A variable whose values are measured or counted. (Helpful: if it makes sense to calculate the mean of the data set, then the variable must be quantitative.)

The 1.5 x IQR Rule for Outliers

Call an observation an outlier if it falls more than 1.5 x IQR above the third quartile or below the first quartile.

1st Quartile (Q1) and 3rd Quartile (Q3)

If the observations in a data set are ordered from lowest to highest, Q1 is the median of the observations that are LEFT of the overall median, and Q3 is the median of the observations that are right of the overall median.

Conditional Distribution (of a variable)

In a two-way table, it describes the distribution of that variable among individuals who have a specific value of the other variable.

Two-way Table

Organizes data in regards to two categorical variables.

Variance

The square of the standard deviation.

Frequency Distribution

Tells what values a variable takes and how often it takes these values. (Note: a relative frequency distribution converts the frequencies to percentages.)

Mode

The value or class in a distribution having the greatest frequency.

Frequency Table

Displays the count of observations in each category or class.

Histogram

Displays the distribution of a quantitative variable. Each bar in the graph represents an equal-width class. The bar height is the class frequency or relative (%) frequency. DO NOT CONFUSE A HISTOGRAM WITH A BAR GRAPH.

Mean

The arithmetic average of a quantitative set of data. Divide the sum of the values of the number of values.