Probability and Statistics Chapter 3

Distribution

Distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence. Consider a simple experiment in which we flip a coin two times.

Marginal Distribution

Below, a two-way table shows the favorite leisure activities for 50 adults - 20 men and 30 women. Because entries in the table are frequency counts, the table is a frequency table . Dance Sports TV Total Men 2 10 8 20 Women 16 6 8 30 Total 18 16 16 50 Entries in the "Total" row and "Total" column are called marginal frequencies or the marginal distribution. Entries in the body of the table are called joint frequencies.

Pie Charts

Show the whole group of cases as a circle. They slice the circle into pieces whose sizes are proportional to the fraction of the whole in each category.

Area Principle

The area principle states that the area of a graph should equal the magnitude of the data it is representing.

Categorical Data Condition

The data are counts or percentages of individuals in categories.

Bar Chart

A bar chart is made up of columns or rows plotted on a graph. Here is how to read a bar chart made up of columns.

Percentages

A percentage is another way of expressing a proportion . A percentage is equal to the proportion times 100.

Proportion

A proportion refers to the fraction of the total that possesses a certain attribute.

Contingency Table

A two-way table (also called a contingency table) is a useful tool for examining relationships between categorical variables. The entries in the cells of a two-way table can be frequency counts or relative frequencies (just like a one-way table ).

Conditional Distributions

A two-way table (also called a contingency table) is used to examine relationships between categorical variables. The entries in the cells of a two-way table can be frequency counts or relative frequencies (just like a one-way table ). Dance Sports TV Total Men 0.04 0.20 0.16 0.40 Women 0.32 0.12 0.16 0.60 Total 0.36 0.32 0.32 1.00 Relative Frequency of Table The table above shows preferences for leisure activities in the form of relative frequencies. The relative frequencies in the body of the table are called conditional frequencies or the conditional distribution. The table above shows relative frequencies for the whole table. Two-way tables can also show relative frequencies separately for the for rows and for columns. The table below shows relative frequencies for rows. Dance Sports TV Total Men 0.10 0.50 0.40 1.00 Women 0.53 0.20 0.27 1.00 Total 0.36 0.32 0.32 1.00 Relative Frequency of Row And the next table shows relative frequencies for columns. Dance Sports TV Total Men 0.11 0.62 0.50 0.40 Women 0.89 0.38 0.50 0.60 Total 1.00 1.00 1.00 1.00 Relative Frequency of Column

Independent Variable

An independent variable, sometimes called an experimental or predictor variable, is a variable that is being manipulated in an experiment in order to observe the effect on a dependent variable, sometimes called an outcome variable.

Relative Frequency Bar Chart

The relative frequency bar chart looks the same as the bar chart but shows the proportion (percentages) of people in each category rather than the counts.

Frequency Table

When a table shows frequency counts for a categorical variable, it is called a frequency table Below, the bar chart and the frequency table display the same data.

Relative Frequency Table

When a table shows relative frequencies for different categories of a categorical variable, it is called a relative frequency table.

Association

When we see evidence that one variable depends on another, we say there's an association between them.