# Stats without Tears

Solutions for Chapter 2

Updated 5 June 2014
(What’s New?)

Copyright © 2013–2020 by Stan Brown

Solutions for Chapter 2

Updated 5 June 2014
(What’s New?)

Copyright © 2013–2020 by Stan Brown

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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.

(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.

(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

**5 June 2014**: Fix a typo, thanks to Kathleen Kelly.- (intervening changes suppressed)
**3 June 2013**: New document.

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Updates and new info: https://BrownMath.com/swt/