BANA CH 2

cumulative relative frequency distribution

shows the proportion of data items

Displays used to show the distribution of data

1. Bar chart 2. Pie Chart 3. Dot Plot 4. Histogram 5. Stem-and-leaf display

The three steps necessary to define the classes for a frequency distribution with quantitative data are

1. Determine the number of nonoverlapping classes. 2. Determine the width of each class. 3. Determine the class limits.

Displays used to show relationships

1. Scatter diagram 2. Trendline

Displays used to make comparisons

1. Side-by-side bar chart 2. Stacked bar charts

Histogram

A common graphical display of quantitative data This graphical display can be prepared for data previously summarized in either a frequency, relative frequency, or percent frequency distribution. A histogram is constructed by placing the variable of interest on the horizontal axis and the frequency, relative frequency, or percent frequency on the vertical axis

Frequency Distribution

A frequency distribution shows the number (frequency) of observations in each of several nonoverlapping classes

Dot plot

A horizontal axis shows the range for the data. Each data value is represented by a dot placed above the axis dot plots show the details of the data and are useful for comparing the distribution of the data for two or more variables

Determining number of classes

Classes are formed by specifying ranges that will be used to group the data. As a general guideline, we recommend using between 5 and 20 classes.

For a data set with n observations, the relative frequency of each class can be determined as follows

Frequency of class/n

Types of Relationships between quantitative variables

Positive, no relationships, and negative

Cumulative Frequency Distribution

The cumulative frequency distribution uses the number of classes, class widths, and class limits developed for the frequency distribution. However, rather than showing the frequency of each class, the cumulative frequency distribution shows the number of data items with values less than or equal to the upper class limit of each class

Width of the classes

The second step in constructing a frequency distribution for quantitative data is to choose a width for the classes. As a general guideline, we recommend that the width be the same for each class. Thus the choices of the number of classes and the width of classes are not independent decisions. Approximate class width = (Largest data value - smallest data value) / number of classes

2. Trendline

Used to approximate the relationship of data in a scatter diagram

2. Stacked bar charts

Used to compare the relative frequency or percent frequency of two categorical variables

1. Side-by-side bar charts

Used to compare two variables

5. Stem and leaf display

Used to show both the rank order and shape of the distribution for quantitative data

3. Dot plot

Used to show the distribution for quantitative data over the entire range of the data

1. Bar chart

Used to show the frequency distribution and relative frequency distribution for categorical data

4. Histogram

Used to show the frequency distribution for quantitative data over a set of class intervals

1. Scatter diagram

Used to show the relationship between two quantitative variables

2. Pie chart

Used to show the relative frequency and percent frequency for categorical data

Scatter Diagram

a graphical display of the relationship between two quantitative variables

Trendline

a line that provides an approximation of the relationship

Relative frequency distribution

gives a tabular summary of data showing the relative frequency for each class

Bar Chart

is a graphical display for depicting categorical data summarized in a frequency, relative frequency, or percent frequency distribution. On one axis of the chart (usually the horizontal axis), we specify the labels that are used for the classes (categories). A frequency, relative frequency, or percent frequency scale can be used for the other axis of the chart (usually the vertical axis). For categorical data, the bars should be separated to emphasize the fact that each category is separate.

Stem and leaf display

is a graphical display used to show simultaneously the rank order and shape of a distribution of data To develop a stem-and-leaf display, we first arrange the leading digits of each data value to the left of a vertical line. To the right of the vertical line, we record the last digit for each data value

Crosstabulation

is a tabular summary of data for two variables. Although both variables can be either categorical or quantitative, crosstabulations in which one variable is categorical and the other variable is quantitative are just as common

Data Visualization

is a term often used to describe the use of graphical displays to summarize and present information about a data set

relative frequency

of a class equals the fraction or proportion of observations belonging to a class

Pie Chart

provides another graphical display for presenting relative frequency and percent frequency distributions for categorical data. To construct a pie chart, we first draw a circle to represent all the data. Then we use the relative frequencies to subdivide the circle into sectors, or parts, that correspond to the relative frequency for each class

cumulative percent frequency distribution

shows the percentage of data items with values less than or equal to the upper limit of each class

Percent frequency distribution

summarizes the percent frequency of the data for each class

Class midpoint

the value halfway between the lower and upper class limits. For the audit time data