Chapter Organizing and Summarizing Data © 2010 Pearson Prentice Hall. All rights reserved 3 2

Section 2.3 Additional Displays of Quantitative Data Objectives 1.Construct frequency polygons 2.Create cumulative frequency and relative frequency tables 3.Construct frequency and relative frequency ogives 4.Draw time-series graphs © 2010 Pearson Prentice Hall. All rights reserved 2-2

Objective 1 Construct frequency polygons © 2010 Pearson Prentice Hall. All rights reserved 2-3

The class midpoint is found by adding consecutive lower class limits and dividing the result by 2. A frequency polygon is drawn by plotting a point above each class midpoint on a horizontal axis at a height equal to the frequency of the class. After the points for each class are plotted, draw straight lines between consecutive points. © 2010 Pearson Prentice Hall. All rights reserved 2-4

Time between Eruptions (seconds) Class Midpoint FrequencyRelative Frequency 670 – – – – – – – © 2010 Pearson Prentice Hall. All rights reserved 2-5

Time (seconds) Frequency Polygon © 2010 Pearson Prentice Hall. All rights reserved 2-6

Time (seconds) Frequency Polygon © 2010 Pearson Prentice Hall. All rights reserved 2-7

Objective 2 Create cumulative frequency and relative frequency tables © 2010 Pearson Prentice Hall. All rights reserved 2-8

A cumulative frequency distribution displays the aggregate frequency of the category. In other words, for discrete data, it displays the total number of observations less than or equal to the category. For continuous data, it displays the total number of observations less than or equal to the upper class limit of a class. A cumulative relative frequency distribution displays the aggregate proportion (or percent) of observations less than or equal to the category. © 2010 Pearson Prentice Hall. All rights reserved 2-9

© 2010 Pearson Prentice Hall. All rights reserved 2-10

Objective 3 Construct frequency and relative frequency ogives © 2010 Pearson Prentice Hall. All rights reserved 2-11

An ogive (read as “oh jive”) is a graph that represents the cumulative frequency or cumulative relative frequency for the class. It is constructed by plotting points whose x-coordinates are the upper class limits and whose y-coordinates are the cumulative frequencies or cumulative relative frequencies. After the points for each class are plotted, draw straight lines between consecutive points. An additional line segment is drawn connecting the upper limit of the class that would preceed the first class (if it existed). © 2010 Pearson Prentice Hall. All rights reserved 2-12

Time (seconds) Frequency Ogive © 2010 Pearson Prentice Hall. All rights reserved 2-13

Time (seconds) Relative Frequency Ogive © 2010 Pearson Prentice Hall. All rights reserved 2-14

Objective 4 Draw time series graphs © 2010 Pearson Prentice Hall. All rights reserved 2-15

If the value of a variable is measured at different points in time, the data is referred to as time series data. A time series plot is obtained by plotting the time in which a variable is measured on the horizontal axis and the corresponding value of the variable on the vertical axis. Lines are then drawn connecting the points. © 2010 Pearson Prentice Hall. All rights reserved 2-16

YearClosing Value , , , , The data to the right shows the closing prices of the Dow Jones Industrial Average for the years 1990 – © 2010 Pearson Prentice Hall. All rights reserved 2-17

Year Closing Value Dow Jones Industrial Average (1990 – 2007) © 2010 Pearson Prentice Hall. All rights reserved 2-18