Stats without Tears
Solutions for Chapter 2

1

2

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.

3

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

Score	Grade	Tallies	Frequency
13.5–15	A	||	2
12–13.4	B	|	1
10.5–11.9	C	||||	5
9–10.4	D	|||	3
0–8.9	F	||||	4

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.)

4

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

5

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

6

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.

8

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.

10

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

• The bars are labeled at their edges, not their centers, because this is a grouped histogram.
• Both axes are titled.
• The horizontal axis has a real-world title. (Sometimes you also need an overall title for the graph, but here the axis title says all that needs to be said.)

(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