Chapter 2 Homework - STA2023 : STEWART

Recent home sales in a suburb of Washington, D.C., are shown in the accompanying ogive. Approximate the percentage of houses that sold for more than $500,000.

60 % EXP - Draw a vertical line from about 500 on the x axis; this crosses the ogive at approximately 0.4. So about 40% of the houses sold for less than $500,000, which implies that about 60% sold for more than $500,000.

Fifty pro-football rookies were rated on a scale of 1 to 5, based on performance at a training camp as well as on past performance. A ranking of 1 indicated a poor prospect whereas a ranking of 5 indicated an excellent prospect. The following frequency distribution was constructed. 1 4 2 10 3 14 4 18 5 4 A-1. How many of the rookies received a rating of 4 or better? A-2. How many of the rookies received a rating of 2 or worse? B-1. Construct the corresponding relative frequency distribution. (Round your answers to 2 decimal places) - 1 : ____ - 2 : ___ - 3 : ___ - 4 : ___ - 5 : ___ B-2. What percent received a rating of 5? C. Construct a bar chart for these data.

A-1: 22 (18+4) A-2: 14 (10+4) B-1: - 0.08 (4/50) - 0.20 - 0.28 - 0.36 - 0.08 B-2: 8% (0.08 X 100) C. Use B-1 answers for the bar chart

A. Construct a stem-and-leaf diagram. B. Is the distribution symmetric?

A. 2 - 4 5 8 3 - 0 2 4 5 6 7 8 4 - 2 4 4 4 7 8 9 5 - 6 7 7 B. Yes; There are the same number of observations on each end of the data and the same number of observations in the middle.

The following ogive summarizes the median household income for the 50 states in the United States (U.S. Census, 2010). A. Approximate the percentage of states with median household income less than $50,000. B. Approximate the percentage of states with median household income more than $60,000.

A. 40% EXP - Draw a vertical line through Income of 50. It intercepts with the ogive at the point of about 0.4. Thus, about 40% of the states had median household income less than $50,000. B. 20% EXP - Draw a vertical line through Income of 60. It intercepts with the ogive at the point of about 0.80. Thus, about 80% of the states had median household income less than $60,000. It is equivalent that about 20% of the states had median household of more than $60,000.

Consider the following cumulative frequency distribution: 15 up to 25 65 25 up to 35 85 35 up to 45 160 45 up to 55 225 A. Construct the frequency distribution. 15 up to 25 25 up to 35 35 up to 45 45 up to 55 C. What percent of the observations are less than 25? (Round your answer to 1 decimal.) Percent of observations:

A. 65(85-65); 20; 75; 65 B. 29% (CF)/TOTAL)

The number of text messages sent by 25 13-year-olds over the past month are as follows: A. Construct frequency distribution using classes of 500 up to 600, 600 up to 700, etc. Texts 500 up to 600 600 up to 700 700 up to 800 800 up to 900 900 up to 1000 B. Construct the relative frequency distribution and the cumulative relative frequency distribution. C-1. How many of the 13-year-olds sent at least 700 but less than 800 text messages? C-2. How many sent less than 700 text messages? D-1. What percent of the 13-year-olds sent at least 700 but less than 800 text messages? D-5. What percent of the 13-year-olds sent less than 900 text messages?

A. 7,7,7,3,1; Total = 25 B. Relative Frequency - Frequency/ Total values of data; Cumulative Frequency: 7 7+7 = 14 14+7 = 21 21+3 = 24 24+1 = 25; Cumulative Relative Frequency: Cumulative Frequency/Total values of data C-1. 7 C-2. 14 D-1. 28% (0.28x100) D-5. 96% (0.96x100)

First-time patients at North Shore Family Practice are required to fill out a questionnaire that gives the doctor an overall idea of each patient's health. The first question is: "In general, what is the quality of your health?" The patient chooses Excellent, Good, Fair, or Poor. Over the past month, the responses to this question from first-time patients were: A. Excellent 4 0.167 Good 5 0.208 Fair 6 0.250 Poor 9 0.375 B. What is the most common response to the questionnaire?

A. Answers in the question B. A - Poor

A. Is the distribution symmetric? If not, is it positively or negatively skewed? B. What percentage of the states had median household income between $45,000 and $55,000? C. What percentage of the states had median household income between $35,000 and $55,000?

A. No. The distribution is positively skewed. B. 44% (0.44x100) C. 66% (0.22+0.44 then times 100)

In a USA TODAY/Gallup Poll, respondents favored Barack Obama over Mitt Romney in terms of likeability, 63% to 25% (Los Angeles Times, July 28, 2012). a. What percentage of respondents favored neither Obama nor Romney in terms of likeability? - Percentage of respondents: b. For a given survey of 500, how many more respondents favored Obama than Romney? - Number of respondents:

A: 12% B: 190

When constructing a frequency distribution for quantitative data, it is important to remember that ______. A. Classes are mutually B. Classes are collectively exhaustive C. The total number of classes usually ranges from 5 to 20 D. All of the above

All of the above EXP - Check the guidelines for constructing a frequency distributions: classes should be mutually exclusive, exhaustive, and the total number of classes should be between 5 and 20.

How does an ogive differ from a polygon?

An ogive is a graphical depiction of a cumulative frequency or cumulative relative frequency distribution, while a polygon is a graphical depiction of a frequency or relative frequency distribution. EXP - An ogive is used to show cumulative frequencies and polygon is graphical depiction of just a frequency.

The accompanying chart shows the numbers of books written by each author in a collection of cookbooks. What type of chart is this?

Bar chart for qualitative data EXP - The data are qualitative and the chart is a bar chart.

When displaying quantitative data, what is an ogive used to plot?

Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class. EXP - An ogive shows cumulative frequency or cumulative relative frequency.

In order to summarize qualitative data, a useful tool a ______.

Frequency distribution. Exp. - Histograms and stem-and-leaf diagrams describe quantitative data.

What graphical tool is best used to display the relative frequency of grouped quantitative data?

Histogram EXP - Histograms are used to display the relative frequency of quantitative data. An ogive is used to display the cumulative frequency, while the bar chart and pie chart display qualitative data.

Which of the following best describes a frequency distribution for qualitative data?

It groups data into categories and records the number of observations in each category. EXP - A frequency distribution for qualitative data groups data into categories and records the number of observations in each category.

In the following pie chart representing a collection of cookbooks, which author has more titles?

Julia Child EXP - The color corresponding to Julia Child has the largest in the pie chart.

For which of the following data sets will a pie chart be most useful?

Percentage of net sales by product for Lenovo in Year 1 EXP - Only percentage of net sales by product for Lenovo in Year 1 looks at multiple categories of a single qualitative variable, in which the percentage of net sales by product may be meaningfully displayed.

A stem-and-leaf diagram is constructed by separating each value of a data set into two parts. What are these parts?

Stem consisting of the leftmost digits and the leaf consists of the remaining digits. EXP - Stem in the stem-and-leaf diagrams consists of the leftmost digits. Leaf consists of the last digit(s).

In the accompanying stem-and-leaf diagram, the values in the stem-and-leaf portions represent 10s and 1s digits, respectively. The stem-and-leaf diagram shows that the distribution is ______.

positively skewed EXP - A stem-and-leaf diagram is basically a histogram on its side. When turned, it reveals a distribution with a few extreme values to the right. Thus, it is positively skewed.