AP stats 1A-1C

Four steps of the statistical problem-solving process

1. Formulate questions

2. Collect data

3. Analyze data

4. Interpret results

Valid statistical investigative question

A question based on data that varies.

Population

The entire group of individuals we want information about.

Census

Collects data from every item or individual in the population.

Sample

A subset of individuals in the population from which we collect data.

Parameter

A number that describes some characteristic of a population.

Statistic

A number that describes some characteristic of a sample.

Observational unit

An item or individual described in a data set or statistical study.

Variable

A characteristic that can take different values for different observational units.

Categorical variable

Takes values that are labels, placing each item or individual into a category.

Quantitative variable

Takes number values that are quantities—counts or measurements.

Discrete quantitative variable

Can take a set of possible values with gaps on the number line, usually resulting from counting.

Continuous quantitative variable

Can take any value in an interval on the number line, usually resulting from measuring.

Distribution of a variable

Tells us what values the variable takes and how often it takes each value.

Frequency table

Shows the number of observational units having each value of a variable.

Relative frequency table

Shows the proportion or percentage of observational units having each value of a variable.

Bar chart

Graph for a categorical variable showing each category as a bar whose height shows frequency or relative frequency.

Pie chart

Graph for a categorical variable showing each category as a slice where area is proportional to its frequency/relative frequency.

Side-by-side bar chart

Displays data for a categorical variable across two or more groups with separate bars for each group.

Dotplot

Graph for a quantitative variable that displays each data value as a dot above a number line.

Roughly symmetric distribution

The right side of the graph is approximately a mirror image of the left side.

Skewed left distribution

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

Skewed right distribution

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

Uniform distribution

A distribution where the frequency or relative frequency of each possible value is about the same.

Unimodal distribution

A distribution of quantitative data with one clear peak.

Bimodal distribution

A distribution of quantitative data with two clear peaks.

Outlier

A value that is unusually small or unusually large relative to the rest of the data.

Variability (Spread)

The dispersion or spread of data values in a distribution.

Stem-and-leaf plot

Graph for a quantitative variable showing each data value split into a stem (leftmost digits) and leaf (final digit).

Histogram

Graph for a quantitative variable displaying intervals of values (bins) as bars where height shows frequency or relative frequency.

Bar chart vs. Histogram

Bar charts display categorical variables (categories on x-axis); histograms display quantitative variables (intervals on x-axis).