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

Section 2.1 Organizing Qualitative Data Objectives 1.Organize Qualitative Data 2.Construct Bar Graphs 3.Construct Pie Charts 2-2© 2010 Pearson Prentice Hall. All rights reserved

When data is collected from a survey or designed experiment, they must be organized into a manageable form. Data that is not organized is referred to as raw data. Ways to Organize Data Tables Graphs Numerical Summaries (Chapter 3) 2-3© 2010 Pearson Prentice Hall. All rights reserved

Objective 1 Organize Qualitative Data in Tables 2-4© 2010 Pearson Prentice Hall. All rights reserved

A frequency distribution lists each category of data and the number of occurrences for each category of data. 2-5© 2010 Pearson Prentice Hall. All rights reserved

EXAMPLE Organizing Qualitative Data into a Frequency Distribution The data on the next slide represent the color of M&Ms in a bag of plain M&Ms. Construct a frequency distribution of the color of plain M&Ms. 2-6© 2010 Pearson Prentice Hall. All rights reserved

The relative frequency is the proportion (or percent) of observations within a category and is found using the formula: A relative frequency distribution lists the relative frequency of each category of data. 2-7© 2010 Pearson Prentice Hall. All rights reserved

EXAMPLE Organizing Qualitative Data into a Relative Frequency Distribution Use the frequency distribution obtained in the prior example to construct a relative frequency distribution of the color of plain M&Ms. 2-8© 2010 Pearson Prentice Hall. All rights reserved

Frequency table 2-9© 2010 Pearson Prentice Hall. All rights reserved

Relative Frequency © 2010 Pearson Prentice Hall. All rights reserved

Objective 2 Construct Bar Graphs 2-11© 2010 Pearson Prentice Hall. All rights reserved

A bar graph is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. 2-12© 2010 Pearson Prentice Hall. All rights reserved

Use the M&M data to construct (a) a frequency bar graph and (b) a relative frequency bar graph. EXAMPLEConstructing a Frequency and Relative Frequency Bar Graph 2-13© 2010 Pearson Prentice Hall. All rights reserved

2-14© 2010 Pearson Prentice Hall. All rights reserved

2-15© 2010 Pearson Prentice Hall. All rights reserved

A Pareto chart is a bar graph where the bars are drawn in decreasing order of frequency or relative frequency. 2-16© 2010 Pearson Prentice Hall. All rights reserved

Pareto Chart 2-17© 2010 Pearson Prentice Hall. All rights reserved

2-18© 2010 Pearson Prentice Hall. All rights reserved EXAMPLEComparing Two Data Sets The following data represent the marital status (in millions) of U.S. residents 18 years of age or older in 1990 and Draw a side-by-side relative frequency bar graph of the data. Marital Status Never married Married Widowed Divorced

2-19© 2010 Pearson Prentice Hall. All rights reserved Relative Frequency Marital Status Marital Status in 1990 vs

(e) Not sure

The side-by-side bar graph shows the revenue of a company for each quarter for two different years. (e) Not sure

Objective 3 Construct Pie Charts

A pie chart is a circle divided into sectors. Each sector represents a category of data. The area of each sector is proportional to the frequency of the category.

EXAMPLEConstructing a Pie Chart The following data represent the marital status (in millions) of U.S. residents 18 years of age or older in Draw a pie chart of the data. Marital StatusFrequency Never married55.3 Married127.7 Widowed13.9 Divorced22.8

Section 2.2 Organizing Quantitative Data: The Popular Displays Objectives 1.Organize discrete data in tables 2.Construct histograms of discrete data 3.Organize continuous data in tables 4.Construct histograms of continuous data 5.Draw stem-and-leaf plots 6.Draw dot plots 7.Identify the shape of a distribution

The first step in summarizing quantitative data is to determine whether the data is discrete or continuous. If the data is discrete and there are relatively few different values of the variable, the categories of data will be the observations (as in qualitative data). If the data is discrete, but there are many different values of the variable, or if the data is continuous, the categories of data (called classes) must be created using intervals of numbers.

Objective 1 Organize discrete data in tables

EXAMPLE Constructing Frequency and Relative Frequency Distribution from Discrete Data The following data represent the number of available cars in a household based on a random sample of 50 households. Construct a frequency and relative frequency distribution Data based on results reported by the United States Bureau of the Census.

Objective 2 Construct histograms of discrete data

A histogram is constructed by drawing rectangles for each class of data whose height is the frequency or relative frequency of the class. The width of each rectangle should be the same and they should touch each other.

EXAMPLE Drawing a Histogram for Discrete Data Draw a frequency and relative frequency histogram for the “number of cars per household” data.

Objective 3 Organize continuous data in tables

Categories of data are created for continuous data using intervals of numbers called classes.

The following data represents the number of persons aged who are currently work disabled. The lower class limit of a class is the smallest value within the class while the upper class limit of a class is the largest value within the class. The lower class limit of first class is 25. The lower class limit of the second class is 35. The upper class limit of the first class is 34. The class width is the difference between consecutive lower class limits. The class width of the data given above is = 10.

EXAMPLEOrganizing Continuous Data into a Frequency and Relative Frequency Distribution The following data represent the time between eruptions (in seconds) for a random sample of 45 eruptions at the Old Faithful Geyser in California. Construct a frequency and relative frequency distribution of the data. Source: Ladonna Hansen, Park Curator

The smallest data value is 672 and the largest data value is 738. We will create the classes so that the lower class limit of the first class is 670 and the class width is 10 and obtain the following classes:

Chapter 2 Section 2 What is the class width in the following frequency distribution? ClassFrequency 1 – – 85 9 – – 163

Objective 4 Construct histograms of continuous data

EXAMPLE Constructing a Frequency and Relative Frequency Histogram for Continuous Data Using class width of 10:

Using class width of 5:

Objective 5 Draw stem-and-leaf plots

A stem-and-leaf plot uses digits to the left of the rightmost digit to form the stem. Each rightmost digit forms a leaf. For example, a data value of 147 would have 14 as the stem and 7 as the leaf.

EXAMPLEConstructing a Stem-and-Leaf Plot An individual is considered to be unemployed if they do not have a job, but are actively seeking employment. The following data represent the unemployment rate in each of the fifty United States plus the District of Columbia in June, 2008.

StateUnemployment Rate StateUnemployment Rate StateUnemployment Rate Alabama4.7Kentucky6.3North Dakota3.2 Alaska6.8Louisiana3.8Ohio6.6 Arizona4.8Maine5.3Oklahoma3.9 Arkansas5.0Maryland4.0Oregon5.5 California6.9Mass5.2Penn5.2 Colorado5.1Michigan8.5Rhode Island7.5 Conn5.4Minnesota5.3South Carolina6.2 Delaware4.2Mississippi6.9South Dakota2.8 Dist Col6.4Missouri5.7Tenn6.5 Florida5.5Montana4.1Texas4.4 Georgia5.7Nebraska3.3Utah3.2 Hawaii3.8Nevada6.4Vermont4.7 Idaho3.8New Hamp4.0Virginia4.0 Illinois6.8New Jersey5.3Washington5.5 Indiana5.8New Mexico3.9W. Virginia5.3 Iowa4.0New York5.3Wisconsin4.6 Kansas4.3North Carolina 6.0Wyoming3.2

We let the stem represent the integer portion of the number and the leaf will be the decimal portion. For example, the stem of Alabama will be 4 and the leaf will be 7.

A split stem-and-leaf plot: This stem represents 3.0 – 3.4 This stem represents 3.5 – 3.9

Once a frequency distribution or histogram of continuous data is created, the raw data is lost (unless reported with the frequency distribution), however, the raw data can be retrieved from the stem-and-leaf plot. Advantage of Stem-and-Leaf Diagrams over Histograms

For the stem-and-leaf plot below, what is the minimum and what is the maximum entry? (a)min: 13; max: 40(b) min: 0; max: 9 (c) min: 13; max: 47 (d) min: 18; max: 39(e) not sure 1|3 represents 13

Objective 6 Draw dot plots

A dot plot is drawn by placing each observation horizontally in increasing order and placing a dot above the observation each time it is observed.

EXAMPLE Drawing a Dot Plot The following data represent the number of available cars in a household based on a random sample of 50 households. Draw a dot plot of the data Data based on results reported by the United States Bureau of the Census.

Objective 7 Identify the shape of a distribution

EXAMPLEIdentifying the Shape of the Distribution Identify the shape of the following histogram which represents the time between eruptions at Old Faithful.

Describe the shape of the distribution. (a) Skewed left(b) Skewed right(c) Symmetric(d) not sure