Practice Quiz with Solutions: Chapter 2 / MATH200 (TC3, Brown)

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.)

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.

histogram of data given in this question

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?

  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 = 78

3(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

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:

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

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

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 _____________________.

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Practice Quiz with Solutions: Chapter 2 (22 min)