**Before looking at these solutions,** please work the
practice quiz.

**Disclaimer:** This quiz is representative of the level of
difficulty you should expect, but it doesn’t include every single
topic from the week’s work. The real quiz may include some other
topics and may skip some that are in this practice quiz. (The real
quiz also may not word questions in the same way as the practice
quiz. You should focus on the concepts, not a particular form of
words.)

**See also:**
How to Take a Math Test

These solutions show about the same level of work I expect from you, though I often add some extra commentary. Please see Show Your Work for the what, why, and how.

1(points: 2) Abigail asked a number of students their major. She
found 35 in liberal arts, 10 in criminal justice, 25 in nursing,
45 in business, and 20 in other majors. What was the relative
frequency of the nursing group, rounded to the nearest whole percent?

**Solution:**
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%

**Common mistake:**
Some students divide 135/25 instead of 25/135. Relative
frequency is always a decimal less than 1 (or a percent less than
100%).

**Common mistake:**
Some students give the answer as 135/5 = 27.
That’s the mean, but that’s not what the problem was asking for.

2(points: 1) Bert asked his fellow students how many books they read for pleasure in a year. He found that most of them read 0, 1, or 2 books, but some read 3 or more and a very few read as many as 10. (He plotted the histogram shown at right.) What is the word or short phrase we learned to describe the shape of this distribution?

**Answer:**
skewed to the right

Exam Scores 5 | 5 6 | 0 4 9 5 7 | 8 4 7 2 8 | 3 7 1 1 7 9 | 9 1 4 Key: 7|8 = 783(points: 3) Here are some exam scores. Make a stem-and-leaf diagram. (You need not sort the leaves.)

83 78 99 60 87 74 64 55 81 81 87 91 69 77 94 65 72

**Answer:**
shown at right

Test scores, x | Frequencies, f |
---|---|

470.0–479.9 | 15 |

480.0–489.9 | 22 |

490.0–499.9 | 29 |

500.0–509.9 | 50 |

510.0–519.9 | 38 |

4(points: 5) At right is a grouped frequency distribution. Create a frequency histogram. (For a real quiz, you’d use graph paper, but you can freehand this one.)

**Answer:**
See the histogram at left. (You can click it to see a larger version.) Important features:

- The
bars are labeled at their edges, not their centers, because this is a
*grouped*histogram. - Both axes are labeled.
- The horizontal axis has a real-world label.

See also: Histogram versus Bar Graph.

**Remark**: Axes are always labeled. Add a graph
title when the title of the horizontal axis doesn’t say all
there is to say.

5(points: 1) What is the class width in the previous problem?

**Solution:**
480−470 = 10

**Common mistake:**
479.9−470 = 9.9 is wrong. The class width is
the difference between successive lower bounds.

6(points: 2) Name two types of graph that are suited to displaying
qualitative data.

**Answer:**
pie chart and bar chart

**Common mistake:**
“Histogram” is not an acceptable answer. A histogram
is used for displaying numeric data. On a histogram, the bars touch
and the data have a definite numeric order. With a bar chart, the bars
do not touch, and you can present them in any order you think
helpful.

7(points: 1) On a histogram or bar graph, to make sure the
graph is not misleading, the vertical axis must always
_____________________.

**Answer:**
start at 0

This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.

For updates and new info, go to http://www.tc3.edu/instruct/sbrown/stat/