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BA501 : The Class : Statistics : Graphs : Lesson
On-Line Lesson
Descriptive Graphs Lesson1-1-1

§ Descriptive Graphs §

Lesson 1- Introduction


Descriptive graphs are designed to show the shape of the data. Arranged data is much easier to understand and interpret than data presented in a random manner. You will study frequency distributions, histograms, frequency polygons, ogives, pie charts and Pareto diagrams in this topic. In most cases, you will be able to use Excel to aid you in this process.


§ Frequency Distribution § Histogram § Frequency Polygon §

§ Ogive § Pie Charts § Nominal Data §  Examples §


Frequency Distribution

A frequency distribution is used as the basis for constructing  histograms, frequency polygons and ogives. A frequency distribution is constructed using raw data counts. A relative frequency distribution uses the percentage of data which fall into classes. A class is a range of numbers between which data values fall.

The true/false and fill-in-the-blank questions in the topic lessons are not being graded. They are designed to give positive feedback no matter what answer you give.

Question A frequency distribution and a relative frequency distribution (for the same set of data) would have the same shape. True False (click one)

The relative frequencies of all classes a relative frequencey distribution add to what number?

(insert answer)

Histogram

A histogram is a falling of data into predetermined classes (range of numbers). The graph of a histogram is usually represented with frequency (or relative frequency) on the vertical axis and the classes in order along the horizontal axis. The result is a series of rectangles the vertical height of which is the frequency (or relative frequency) and the horizontal width of which is the class width.

Question For a given set of data, the class widths can vary in size. True False (click one)

The class ______ are the numbers used to define a class width.
(insert answer)

Frequency Polygon

A frequency polygon graphical representation of frequency (or relative frequency) of data without using rectangles as in a histogram. All the steps necessary to construct a histogram are followed, then the class midpoints of the top of the histogram rectangles are connected. Next, the ends of the line connecting the class midpoints are extend down to the horizontal axis. The left extension is to the midpoint of the next empty class to the left. The right extension is to the midpoint of the next empty class to the right.

Question Histograms and frequency polygons are different ways of showing the same information. True False (click one)

A frequency polygon is completely ________ on all sides.
(insert answer)

 

Ogive

An ogive is a graphical representation of the cumulative frequency (or cumulative relative frequency) of data. The otherwise histogram rectangles are stacked on top of each other (the left most stacked on the next rectangle to the right, then both of these stacked on the next rectangle to the right, etc.) until 100% of the data has been accumulated on the far right. Connect the lower class limit of the first class to the upper class limits the accumulated stacked rectangles to the right until the upper class limit of the last stack indicates 100%. Remove the stacked rectangle. The result is an ogive. An ogive is a graphical way to determine percentiles.

Question An ogive can contructed without modification to a histogram. True False (click one)

An ogive shows the __________ of data accumulated to any point on the horizontal axis (classes).
(insert answer)

Pie Charts

A pie chart is a graphical representation of frequency (or relative frequency) data and/or nominal data as percentages of a circle. Nominal data are simply names or labels (e.g. responses to a survey with selections A, B, C, D, or E). Each one of the letters might represent a statement (e.g. "A" might represent the statement  "strongly agree"). The circle is divided into the percentage parts represented by each category.

Question There are 360 degrees in 100% of a pie chart circle. True False (click one)

180 degress in a pie chart represents what percentage?
(insert answer)

Nominal Data, Frequency, Bar Charts and Pie Charts

As mentioned in the preceding paragraph, a pie chart may be used to display nominal data. In addition, nominal data my be represented by frequency distributions and bar charts. Special techniques are used to include nominal data as a part of a data series.

Question Nominal data is made up of numbers. True False (click one)

Nominal data is made up of what?

Examples- See link below


You should now:

Go on to Lesson 2: Examples
or

Go back to Descriptive Graphs: Activities and Assignments


Please reference "BA501 (your last name) Assignment name and number" in the subject line of either below.

E-mail Dr. James V. Pinto at BA501@mail.cba.nau.edu
or call (928) 523-7356. Use WebMail for attachments.

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