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summary table

indicates the frequency, amount, or percentage of items in a set of categories so that you can see differences between categories.

charts that are often used for categorical data

Bar charts and Pie charts

Length of bar or size of pie slice shows

the frequency or percentage for each category

bar chart

shows each category, the length of which represents the amount, frequency or percentage of values falling into a category.

pie chart

a circle broken up into slices that represent categories. The size of each slice of the pie varies according to the percentage in each category

Pareto Chart

1. Used to portray categorical data (nominal scale)
2. A vertical bar chart, where categories are shown in descending order of frequency
3. A cumulative polygon is shown in the same graph
4. Used to separate the "vital few" from the "trivial many"

ordered array

1. is a sequence of data, in rank order, from the smallest value to the largest value.
2. Shows range (minimum value to maximum value)
3. May help identify outliers (unusual observations)

Stem and Leaf Display

1. A simple way to see how the data are distributed and where concentrations of data exist
2. organizes data into groups (called stems) so that the values within each group (the leaves) branch out to the right on each row

frequency distribution

is a summary table in which the data are arranged into numerically ordered classes

Why Use a Frequency Distribution

1.It condenses the raw data into a more useful form
2. It allows for a quick visual interpretation of the data
3. It enables the determination of the major characteristics of the data set including where the data are concentrated / clustered


1. A vertical bar chart of the data in a frequency distribution is called
2. In a histogram there are no gaps between adjacent bars.

class boundaries

shown on the horizontal axis in a histogram

percentage polygon

formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoints at their respective class percentages.

cumulative percentage polygon

-also called an ogive
-displays the variable of interest along the X axis, and the cumulative percentages along the Y axis.
-Useful when there are two or more groups to compare.

cross tabulations

1. Used to study patterns that may exist between two or more categorical variables.
2. can be presented in Contingency Tables

cross-classification (or contingency) table

presents the results of two categorical variables. The joint responses are classified so that the categories of one variable are located in the rows and the categories of the other variable are located in the columns.

How is a contingency table set up

The cell is the intersection of the row and column and the value in the cell represents the data corresponding to that specific pairing of row and column categories

scatter plots

1. are used for numerical data consisting of paired observations taken from two numerical variables
2. used to examine possible relationships between two numerical variables

Time Series Plot

used to study patterns in the values of a numeric variable over time

How is a time series plot set up?

Numeric variable is measured on the vertical axis and the time period is measured on the horizontal axis

When constructing a frequency distribution, classes should be selected in such a way that they are of equal width. (True of False)


True or False: Percentage polygons are plotted at the boundaries of the class groupings.


True or False: If you wish to construct a graph of a relative frequency distribution, you would most likely construct an ogive first.


True or False: A histogram can have gaps between the bars, whereas bar charts cannot have gaps.


A survey of 150 executives were asked what they think is the most common mistake candidates make during job interviews. Six different mistakes were given. Which of the following is the best for presenting the information?

bar chart

Data on the number of part-time hours students at a public university worked in a week were collected. Which of the following is the best chart for presenting the information?

A percentage polygon

The width of each bar in a histogram corresponds to the

differences between the boundaries of the class.

True or False: The percentage distribution cannot be constructed from the frequency distribution directly.


True or False: Ogives are plotted at the midpoints of the class groupings.


When constructing charts, the following is plotted at the class midpoints:

percentage polygons.

You have collected data on the approximate retail price (in $) and the energy cost per year (in $) of 15 refrigerators. Which of the following is the best for presenting the data?

A scatter diagram

True or False: One of the advantages of a pie chart is that it clearly shows that the total of all the categories of the pie adds to 100%.


You have collected data on the number of U.S. households actively using online banking and/or online bill payment from 1995 to 2007. Which of the following is the best for presenting the data?

a times series plot

True or False: The sum of cumulative frequencies in a distribution always equals 1.


True or False: A polygon can be constructed from a bar chart.


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