APEX AP Stats Lesson 1.2 Overview: Displaying Distributions with Graphs Studyguide

Distribution

the values it takes and how often it takes these values

Categorical Data

aka qualitative data; uses names and labels over numbers; cannot be sorted or manipulated mathematically as numbers

Categorical Variable

related to variable; aka qualitative variable; variable containing categorical data

Class

related to frequency table; A range into which numerical data can be grouped.

Class Boundaries

related to discrete data; the max and min values in each class in a histogram/frequency table; they must be set so that no observation lies directly on a class boundary so that there are the right number of classes; can be definite numbers

Class Interval

distance between 2 successive class minimums in a histogram/frequency table

Class Limits

upper and lower boundaries of a class

Class Width

distance between the max and min of a given class in a histogram or frequency table

Cumulative Frequency

The sum of a series of frequencies in a data set, in which the frequency from one class is added to the sum of the frequencies of all the classes below it. The addition of all frequencies in a data set will equal the total number of observations in a data set.

Cumulative Relative Frequency Graph

related to line graph and class; aka cumulative relative frequency plot; A line graph that shows cumulative relative frequencies on the vertical axis and data values (divided into classes) on the horizontal axis. A cumulative relative frequency graph will look similar to a cumulative frequency graph for the same data set.

Cumulative Frequency Graph

related to class and line graph; aka cumulative frequency plot; A line graph that shows cumulative frequencies on the vertical axis and data values (divided into classes) on the horizontal axis.

Frequency

The number of observations within a range of data.

Frequency Plot

A plot (or graph) that shows frequencies. Stem-and-leaf plots, histograms, and bar charts are types of frequency plots.

Level (of a categorical variable)

aka category; The value, or label, taken on by a categorical variable. For example, in a study of average rainfall in the different states within the United States, the levels of the categorical variable state would be the states: Alaska, Arkansas, and so on. Each state can also be called a category, or value, of the categorical variable state. The levels of a categorical variable typically follow no implicit rank ordering, and the values of this variable should not be mathematically manipulated.

Variable

related to numerical and categorical data; A varying characteristic being studied. For example, in a study that tracks the amount of rainfall per month, the variables would be month and amount of rainfall. Month would be a categorical variable, and amount of rainfall would be a numerical variable.

Dot Plot

related to observation; A dot plot displays the number of observations with a particular value; each observation is shown as a dot.

Frequency Distribution

A frequency distribution shows which numbers are most common, which are least common, the total range of the numbers, and the shape of the distribution.

Line Graph

A line graph is similar to a histogram and a bar chart, where values are shown as points connected by a line, usually used for time-series data collected over uniform time intervals.

Point in Line Graph

In a line graph, a point represents the data value for a level of a variable.

Bar Chart/Bar Graph

A bar chart displays the values associated with each level of the independent variable, used when the horizontal axis represents a categorical or qualitative variable.

Pie Chart

A pie chart, also known as a circle graph, shows the amounts or the number of observations in each level of a given categorical variable.

Relative Frequency Histogram

A relative frequency histogram shows the same pattern as a frequency histogram, but the vertical axis is expressed in decimal values or percentages representing the proportion of observations.

Relative Frequency

Relative frequency is the number of observations within a given class or category, divided by the total number of observations.

Frequency Tables

A frequency table shows the number of observations in each of the classes, categories, or levels of a variable.

Shape of Distribution

The shape of a distribution indicates whether most of the observations are toward the middle or the end of the range.

Total Range of Numbers

The total range of numbers refers to the difference between the highest and lowest values in a dataset.

Rainfall Line Graph

In a rainfall line graph, each point equals the number of inches of rainfall in a city in a given month.

Observations in Dot Plot

In a dot plot, each dot represents one observation with a specific value.

Shortcomings of Dot Plot

Although a dot plot is useful for showing the shape of a frequency distribution, it has some shortcomings.

Histogram

A histogram is a graphical representation of the distribution of numerical data.

Observation

An observation is a single data point collected in a study.

Independent Variable

An independent variable is the variable that is manipulated to observe its effect on the dependent variable.

Dependent Variable

A dependent variable is the variable being tested and measured in an experiment.

Uniform Time Intervals

Uniform time intervals refer to consistent time periods used for collecting data.

Proportion of Observations

The proportion of observations refers to the fraction of the total observations that fall within a specific category.

Wedges in Pie Chart

In a pie chart, larger wedges indicate months with greater rainfall, while smaller wedges indicate months with less rainfall.

Months in Pie Chart

Using a pie chart, you can decide whether most of the rain in a city occurs during a particular season or is spread throughout the year.

Cumulative Frequency Plots

A plot that shows the cumulative frequency of data points in a dataset.

Stem-and-Leaf Plot

A plot that displays the shape of a distribution of a numerical variable while including the actual values.

Stem

The first digit(s) of the values of a numerical variable, representing the first column of a stem-and-leaf plot.

Leaf

The last digit of the value of a numerical variable, added to the right of the vertical line in a stem-and-leaf plot.

Gaps

A class with a frequency of zero, or no observations.

Midpoint (in a histogram)

The middle number of each class, calculated as the mean of the class maximum and minimum.

Numerical Data

Data that appear as numbers and can be manipulated mathematically, including weights, heights, and percentages.

Numerical Variable

A variable containing numerical data, also known as a quantitative variable.

Value

A number or label taken on by a variable, which can take on a range of levels or categories.

Back-to-Back Stem-and-Leaf Plot

A stem-and-leaf plot that displays two sets of data back-to-back for comparison.

Shape

The general form or outline of a distribution in a dataset.

Uniform Distribution

A distribution where all outcomes are equally likely.

J-Shaped Distribution

A distribution that has a shape resembling the letter 'J', indicating a concentration of values at one end.

Mound-Shaped Distribution

A distribution that is symmetric and has a single peak.

U-Shaped Distribution

A distribution that has a shape resembling the letter 'U', indicating concentrations at both ends.

Skewness

A measure of the asymmetry of the probability distribution of a real-valued random variable.

Clusters

Groups of data points that are closely packed together in a dataset.

Line Plot

A plot that displays data points on a number line, often used to show trends over time.

Outliers

Data points that differ significantly from other observations in a dataset.