AP Statistics - Chapter 1: Exploring Data

Individuals

The objects described by a set of data; Individuals may be people, animals or things

Variable

Any charectiristic of an individual. A variable can take different values for different indivuals. There are 2 types of variables - Categorical and Quantitive.

Categorical Variable

Take values that are category names, tables, types, groups, or locations. Ex: Genre of movies

Quantitative Variable

Take numerical values for a measured or counted quanitity. It makes sense to find average value for these variables.

Frequency Table

Displays the counts (frequencies) for how often each value appears

Relative Frequency Table

Data that shows the percents - frequencies are expressed as a proportion of the total number of values in the data set.

Pie Charts

Counts/Percents for the categories. The percents of the categories must make up the (1) whole or 100%

Bar graphs

Percents or counts, bars don’t touch only histogram bars touch and histograms are used for quantitative data.

Symetric

If the right and left sides of the graph are approximately mirror images of each other.

Skewed right

If the right side of the graph is much longer than the left side.

Skewed left

If the right side of the graph is much longer than the right side

Unimodal

A distribution with ONE clear peak

Bimodal

A distribution with two clear peaks

Multimodal

A distribution with multiple peaks

Stemplots

Give quick picture of the shape of a distribution while including the actual numerical values in a graph.

Histrogram

Distribution of a quantitative variable

Dotplots

Each data value is shown as a dot above its location on a number line. Best for small data sets.

Measures of Center

Mean and Median

Mean

Arithmetic Average Value

Median

Describes the midpoint of a distribution. The typical value of the data set, half of the observations are smaller and the other half are larger. Center of an ordered list.

Measures of Spread

Range, IQR, Outliers

Ranger

Max-Min

IQR

Identifies middle 50% of the data

Standard deviation

Most important measure of spread. Measures spread by looking at how far the observations are from the mean. Typicall distance.

Variance

The average squared the deviation from the mean