Topic 2 Problem Set

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1. A company uses a 5-star rating system for its customer reviews, where customers can rate their experience as , , , , or . What kind of variable is this?
2. Last Friday night at the downtown Chicago restaurant Chez Pierre, the owner wrote down how much money was spent (what their bill was) for 28 tables. Those values are below.

110 128 122 99 191 123 76 76 165 102
118 129 139 119 130 149 175 110 67 151
124 185 120 95 84 110 143 83

(a) What kind of data set is this?
(b) What is the sample size?
(c) What was the mean bill? (round to 2 decimal places, a.k.a. the penny)
(d) What was the median bill?
(e) What was the modal bill?
(f) What was the minimum bill?
(g) What was the maximum bill?
(h) What was the range of the bills?
(i) What was the variance of the bills? (round to 2 decimal places)
(j) What was the standard deviation of the bills? (round to 2 decimal places)

3. Professor Crazyguy gave 4 quizzes last semester in his Tax Accounting class, which had 10 students. All of those scores are below.

Student: 1 2 3 4 5 6 7 8 9 10
Quiz 1: 76 76 76 76 87 89 90 91 104 115
Quiz 2: 81 81 81 81 86 90 95 95 95 95
Quiz 3: 82 83 86 87 88 88 90 90 111 115
Quiz 4: 26 65 86 96 101 104 106 109 113 114

(a) What kind of data set is this?
(b) What kind of variables are the quiz scores?
(c) What was the average quiz score all semester? (round to 1 decimal place)
(d) Which quiz had the highest class average?
(e) Based on standard deviations, which quiz had the highest variation in scores?
(f) What was the modal score for Quiz 1?
(g) What was the minimum for Quiz 4?
(h) What was the maximum for Quiz 2?
(i) What was the range for Quiz 3?
(j) What was the median score for Quiz 1? (round to 1 decimal place)

4. Noodles & Company tested consumer reaction to 2 spaghetti sauces. Each of 70 judges rated both sauces on a scale of 1 (worst) to 10 (best) using several taste criteria. To correct for possible bias in tasting order, half the judges tasted Sauce A first, while the other half tasted Sauce B first. The results are below.

Judge Sauce A Sauce B Judge Sauce A Sauce B
1 7 3 36 6 6
2 7 5 37 5 8
3 8 6 38 8 6
4 8 6 39 3 8
5 4 2 40 5 9
6 6 6 41 7 1
7 8 7 42 6 6
8 6 6 43 8 3
9 5 9 44 9 8
10 8 7 45 6 5
11 7 8 46 8 5
12 5 8 47 8 6
13 3 8 48 5 7
14 6 2 49 6 8
15 8 7 50 7 6
16 7 6 51 7 5
17 5 7 52 6 3
18 7 6 52 6 6
19 3 8 54 6 8
20 4 7 55 2 6
21 5 5 56 7 6
22 7 7 57 7 5
23 8 7 58 7 2
24 6 7 59 8 6
25 7 6 60 8 7
26 7 5 61 5 8
27 8 8 62 5 8
28 7 5 63 6 5
29 7 5 64 7 7
30 7 1 65 6 2
31 6 8 66 7 5
32 8 5 67 2 8
33 8 8 68 5 5
34 7 6 69 6 6
35 8 1 70 5 5

(a) What is the sample size?
(b) Which sauce was liked better, on average?
(c) Which sauce had the larger variation in ratings?
(d) Which sauce was liked better, based on the medians?
(e) Which sauce was liked better, based on the modes?
(f) What is the correlation coefficient between the 2 ratings? (round to 3 decimal places)
(g) Interpret the correlation coefficient.