Chapter 2: Visualizations of Data
Chapter Outline
 2.1. Histograms and Frequency Distributions
 2.2. Common Graphs and Data Plots
 2.3. BoxandWhisker Plots
Chapter Summary
Part One: Questions
 Which of the following can be inferred from this histogram?
 The mode is 1.
 mean < median
 median < mean
 The distribution is skewed left.
 None of the above can be inferred from this histogram.
 Sean was given the following relative frequency histogram to read. Unfortunately, the copier cut off the bin with the highest frequency. Which of the following could possibly be the relative frequency of the cutoff bin?
 16
 24
 30
 68
 Tianna was given a graph for a homework question in her statistics class, but she forgot to label the graph or the axes and couldn’t remember if it was a frequency polygon or an ogive plot. Here is her graph: Identify which of the two graphs she has and briefly explain why.
In questions 47, match the distribution with the choice of the correct realworld situation that best fits the graph.

 Endy collected and graphed the heights of all the grade students in his high school.
 Brittany asked each of the students in her statistics class to bring in 20 pennies selected at random from their pocket or piggy bank. She created a plot of the dates of the pennies.
 Thamar asked her friends what their favorite movie was this year and graphed the results.
 Jeno bought a large box of doughnut holes at the local pastry shop, weighed each of them, and then plotted their weights to the nearest tenth of a gram.
 Which of the following box plots matches the histogram?
 If a data set is roughly symmetric with no skewing or outliers, which of the following would be an appropriate sketch of the shape of the corresponding ogive plot?
 Which of the following scatterplots shows a strong, negative association?
Part Two: OpenEnded Questions
 The chart below lists the 14 tallest buildings in the world (as of 12/2007).
Building  City  Height (ft) 

Taipei 101  Tapei  1671 
Shanghai World Financial Center  Shanghai  1614 
Petronas Tower  Kuala Lumpur  1483 
Sears Tower  Chicago  1451 
Jin Mao Tower  Shanghai  1380 
Two International Finance Center  Hong Kong  1362 
CITIC Plaza  Guangzhou  1283 
Shun Hing Square  Shenzen  1260 
Empire State Building  New York  1250 
Central Plaza  Hong Kong  1227 
Bank of China Tower  Hong Kong  1205 
Bank of America Tower  New York  1200 
Emirates Office Tower  Dubai  1163 
Tuntex Sky Tower  Kaohsiung  1140 
(a) Complete the table below, and draw an ogive plot of the resulting data.
Class  Frequency  Relative Frequency  Cumulative Frequency  Relative Cumulative Frequency 

(b) Use your ogive plot to approximate the median height for this data.
(c) Use your ogive plot to approximate the upper and lower quartiles.
(d) Find the percentile for this data (i.e., the height that 90% of the data is less than).
 Recent reports have called attention to an inexplicable collapse of the Chinook Salmon population in western rivers (see http://www.nytimes.com/2008/03/17/science/earth/17salmon.html). The following data tracks the fall salmon population in the Sacramento River from 1971 to 2007.
Year  Adults  Jacks 

19711975  164,947  37,409 
19761980  154,059  29,117 
19811985  169,034  45,464 
19861990  182,815  35,021 
19911995  158,485  28,639 
1996  299,590  40,078 
1997  342,876  38,352 
1998  238,059  31,701 
1998  395,942  37,567 
1999  416,789  21,994 
2000  546,056  33,439 
2001  775,499  46,526 
2002  521,636  29,806 
2003  283,554  67,660 
2004  394,007  18,115 
2005  267,908  8.048 
2006  87,966  1,897 
Figure: Total Fall Salmon Escapement in the Sacramento River. Source: http://www.pcouncil.org/bb/2008/1108/D1a_ATT2_1108.pdf
During the years from 1971 to 1995, only 5year averages are available.
In case you are not up on your salmon facts, there are two terms in this chart that may be unfamiliar. Fish escapement refers to the number of fish who escape the hazards of the open ocean and return to their freshwater streams and rivers to spawn. A Jack salmon is a fish that returns to spawn before reaching full adulthood.
(a) Create one line graph that shows both the adult and jack populations for these years. The data from 1971 to 1995 represent the fiveyear averages. Devise an appropriate method for displaying this on your line plot while maintaining consistency.
(b) Write at least two complete sentences that explain what this graph tells you about the change in the salmon population over time.
 The following data set about Galapagos land area was used in the first chapter.
Island  Approximate Area (sq. km) 

Baltra  8 
Darwin  1.1 
Española  60 
Fernandina  642 
Floreana  173 
Genovesa  14 
Isabela  4640 
Marchena  130 
North Seymour  1.9 
Pinta  60 
Pinzón  18 
Rabida  4.9 
San Cristóbal  558 
Santa Cruz  986 
Santa Fe  24 
Santiago  585 
South Plaza  0.13 
Wolf  1.3 
Figure: Land Area of Major Islands in the Galapagos Archipelago. Source: http://en.wikipedia.org/wiki/Gal%C3%A1pagos_Islands
(a) Choose two methods for representing this data, one categorical, and one numerical, and draw the plot using your chosen method.
(b) Write a few sentences commenting on the shape, spread, and center of the distribution in the context of the original data. You may use summary statistics to back up your statements.
 Investigation: The National Weather Service maintains a vast array of data on a variety of topics. Go to: http://lwf.ncdc.noaa.gov/oa/climate/online/ccd/snowfall.html. You will find records for the mean snowfall for various cities across the US.
 Create a backtoback stemandleaf plot for all the cities located in each of two geographic regions. (Use the simplistic breakdown found at http://library.thinkquest.org/4552/ to classify the states by region.)
 Write a few sentences that compare the two distributions, commenting on the shape, spread, and center in the context of the original data. You may use summary statistics to back up your statements.
Keywords
Backtoback stem plots
Bar graph
Bias
Bivariate data
Boxandwhisker plot
Cumulative frequency histogram
Density curves
Dot plot
Explanatory variable
Fivenumber summary
Frequency polygon
Frequency tables
Histogram
Modified box plot
Moundshaped
Negative linear association
Ogive plot
Pie graph
Positive linear association
Relative cumulative frequency histogram
Relative cumulative frequency plot
Relative frequency histogram
Response variable
Scatterplot
Skewed left
Skewed right
Stemandleaf plot
Symmetric
Tail