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
 32
 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 Burj Dubai will become the world’s tallest building when it is completed. It will be twice the height of the Empire State Building in New York.
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 
The chart lists the 15 tallest buildings in the world (as of 12/2007).
(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/newsreleases/Sacto_adult_and_jack_escapement_thru%202007.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
 Stem plots can also be a useful tool for comparing two distributions when placed next to each other. These are commonly called backtoback stem plots.
 Bar graph
 the bars in a bar graph usually are separated slightly. The graph is just a series of disjoint categories.
 Bias
 The systematic error in sampling is called bias.
 Bivariate data
 The goal of examining bivariate data is usually to show some sort of relationship or association between the two variables.
 Boxandwhisker plot
 A boxandwhisker plot is a very convenient and informative way to represent singlevariable data.
 Cumulative frequency histogram
 A relative cumulative frequency histogram would be the same, except that the vertical bars would represent the relative cumulative frequencies of the data
 Density curves
 The most important feature of a density curve is symmetry. The first density curve above is symmetric and moundshaped.
 Dot plot
 A dot plot is one of the simplest ways to represent numerical data.
 Explanatory variable
 the time in years is considered the explanatory variable, or independent variable.
 Fivenumber summary
 The fivenumber summary is a numerical description of a data set comprised of the following measures (in order): minimum value, lower quartile, median, upper quartile, maximum value.
 Frequency polygon
 A frequency polygon is similar to a histogram, but instead of using bins, a polygon is created by plotting the frequencies and connecting those points with a series of line segments.
 Frequency tables
 to create meaningful and useful categories for a frequency table.
 Histogram
 A histogram is a graphical representation of a frequency table (either actual or relative frequency).
 Modified box plot
 This box plot will show an outlier as a single, disconnected point and will stop the whisker at the previous point.
 Moundshaped
 it has a single large concentration of data that appears like a mountain. A data set that is shaped in this way is typically referred to as moundshaped.
 Negative linear association
 If the ellipse cloud were trending down in this manner, we would say the data had a negative linear association.
 Ogive plot
 This plot is commonly referred to as an ogive plot.
 Pie graph
 data that can be represented in a bar graph can also be shown using a pie graph (also commonly called a circle graph or pie chart).
 Positive linear association
 Data that are oriented in this manner are said to have a positive linear association. That is, as one variable increases, the other variable also increases.
 Relative cumulative frequency histogram
 it is helpful to know how the data accumulate over the range of the distribution.
 Relative cumulative frequency plot
 In a relative cumulative frequency plot, we use the point on the right side of each bin.
 Relative frequency histogram
 A relative frequency histogram is just like a regular histogram, but instead of labeling the frequencies on the vertical axis, we use the percentage of the total data that is present in that bin.
 Response variable
 can be identified as having an impact on the value of the other variable, the response (dependent) variable.
 Scatterplot
 Bivariate data can be represented using a scatterplot to show what, if any, association there is between the two variables.
 Skewed left
 the left tail of the distribution is stretched out, so this distribution is skewed left.
 Skewed right
 The right side of the data is spread out across a wider area. This type of distribution is referred to as skewed right.
 Stemandleaf plot
 A stemandleaf plot is a similar plot in which it is much easier to read the actual data values.
 Symmetric
 A data set that is mound shaped can be classified as either symmetric or skewed.
 Tail
 It is the direction of the long, spread out section of data, called the tail.