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Solutions for Chapter 2

Updated 5 June 2014 (What’s New?)
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← Exercises for Ch 2 

1 bar graph for Mixican attitudes about moving to the US

There’s no scale to interpret the quantities. And if one fruit in each row is supposed to represent a given quantity, then banana and apple have the same frequency, yet banana looks like its frequency is much greater.


90% of 15 is 13.5, 80% is 12, 70% is 10.5, and 60% is 9.


bar graph for the table shown at left
Alternatives: Instead of a title below the category axis, you could have a title above the graph. You could order the grades from worst to best (F through A) instead of alphabetically as I did here. And you could list the class boundaries as 13.5–15, 12–13.5, 10.5–12, and so on, with the understanding that a score of 12 goes into the 12–13.5 class, not the 10.5–12 class. (Data points “on the cusp” always go into the higher class.)


(a) The variable is discrete, “number of deaths in a corps in a given year”.
(b) bar graph for numbers of deaths
Alternatives: Some authors would draw a histogram (bars touching) or even a pie chart. Those are okay but not the best choice.

      Commuting Distance
  0 | 5 9 8 1
  1 | 5 2 2 1 9 6 2 8 7 6 5 7
  2 | 3 2 6 1 6 4 0
  3 | 1
  4 | 5
              Key: 2 | 3 = 23 km

Relative frequency is f/n. f = 25, and n = 35+10+25+45+20 = 135. Dividing 25/135 gives 0.185185… ≈ 0.19 or 19%

7 (a) Bar graph, histogram, stemplot. A bar graph or histogram can be used for any ungrouped discrete data. (Some authors use one, some use the other. I like the bar graph for ungrouped discrete data.) A stemplot, or stem-and-leaf diagram, can be used when you have a moderate data range without too many data points.
(b) Histogram.
(c) Bar graph, pie chart.

skewed right

9 (a) Group the data when you have a lot of different values.
(b) The classes must all be the same width, and there must be no gaps.

histogram of the given data (a) See the histogram at right. Important features:

(b) 480.0−470.0 = 10.0 or just plain “10”.

Don’t make the common mistake of subtracting 479.9−470.0. Subtract consecutive lower bounds, always.

(c) skewed left

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