1.	Below are family income figures (in thousands of dollars) for 15 residents of a neighborhood.  Make a stemplot of the income data.

17	
31	
25	
30	
21	

25	
28	
19	
32	
25	

32	
27	
21	
26	
21	

2.	The data below represent the numbers of auto accidents at a certain intersection each month for a year.  Make a stemplot of the data.

0, 1, 3, 4, 5, 2, 2, 6, 7, 2, 0, 1 	

3.	The 50 measurements given below represent the weights, in ounces, of zucchini grown in a garden one summer.  Make a histogram of the weights using classes of width of 5 oz.  Does the distribution appear to be symmetric?

12	
8	
23	
14	
25	
22	
16	
28	
35	
26	

27	
26	
30	
18	
37	
26	
31	
37	
20	
28	

42	
21	
27	
7	
25	
18	
23	
11	
23	
32	

30	
29	
36	
22	
38	
32	
26	
6	
17	
33	

28	
11	
20	
32	
24	
28	
12	
32	
19	
38	

4.	Below are exam scores for 26 students in an English course.  Make a histogram of the scores.

84	
77	
67	
94	
90	
77	
79	

81	
56	
89	
77	
88	
72	
93	

74	
76	
28	
80	
58	
94	

66	
77	
89	
81	
78	
93	

5.	Below are exam scores for 26 students in an English course.  Find the median exam score.

84	
77	
67	
94	
90	
77	
79	

81	
56	
89	
77	
88	
72	
93	

74	
76	
28	
80	
58	
94	

66	
77	
89	
81	
78	
93	

6.	Below are family income figures (in thousands of dollars) for 15 residents of a neighborhood.  Find the median family income.

17	
31	
25	
30	
21	

25	
28	
19	
32	
25	

32	
27	
21	
26	
21	

7.	Find the mean of the following set of data
 
     23, 45, 26, 18, 11, 42, 35, 16, 32 	

8.	Below are the ages of students attending an art exhibit.  Find the mean age of the students.
 
     11, 11, 12, 12, 13, 1 3, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18 	

9.	Below are the ages of students attending an art exhibit.  Find the first and third quartiles of the data.

11, 11, 12, 12, 13, 1 3, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18 	

10.	A linguist is studying the lengths of paragraphs in a given text. The number of words in 20 paragraphs are given below.  Find the five-number summary for the data.

42	
88	
37	
75	
98	
93	
73	
62	
96	
80	

52	
76	
66	
54	
73	
69	
83	
62	
53	
79	

11.	Find the five-number summary for the following set of data.

2	
11	
6	
4	
18	

1	
9	
2	
2	
15	

8	
16	
12	
11	
17	

12.	Below are the exam scores of 30 students.  Make a boxplot of this data.

24	
31	
38	
49	
51	
55	
56	
59	
62	
63	

65	
66	
69	
72	
72	
74	
76	
81	
84	
84	

86	
86	
86	
88	
88	
88	
91	
91	
92	
99	

13.	Below are the ages of 30 people who died in a city hospital in one month.  Make a boxplot of this data.

7	
22	
25	
31	
37	
38	
41	
48	
49	
50	

55	
58	
62	
62	
64	
65	
66	
66	
72	
75	

76	
76	
76	
85	
86	
88	
88	
88	
92	
94	

14.	Find the variance of the following set of data.

5, 7, 17, 31, 45, 47, 68, 85, 96, 99 	

15.	Below are the ages of six patients seen by a pediatrician on one day.  Find the variance of the ages.

3, 6, 7, 9, 15, 20 	

16.	Two towns both have a mean income for their residents of $30,000.  The standard deviation of incomes of residents in town A is $2600 and the standard deviation of incomes of residents in town B is $25,000.  Explain what this says about the difference in the distribution of incomes in the two towns. 	

17.	Below are the ages of six patients seen by a pediatrician on one day.  Find the standard deviation of the ages.

3, 6, 7, 9, 15, 20 	

18.	Find the standard deviation of the following set of measurements.

4, 7, 9, 11, 13, 22 	

19.	After computing the standard deviation and variance for a set of varying measurements, you notice that the two values are equal.  How is this possible?	

20.	How could it be possible that the standard deviation would be larger than the variance?	

21.	Below is a histogram of car prices on a used car lot.  An advertisement for the lot says the average price of a car for sale is $12,000.  Could the advertisement be true?  Why or why not?

22.	Below is a histogram for a set of data.  Would you use the five-number summary or the mean and standard deviation to describe these data?  Why?

23.	In the list of five measurements shown below, one is blurred.  What must this value be, if the mean of the five measurements is 7?

8	
5	
10	
3	
#	

24.	In the list of five measurements shown below, one is blurred.  What must this value be, if the mean of the five measurements is 6?

8	
5	
10	
3	
#	

25.	In the list of five measurements shown below, one is blurred.  Supply a fifth value that would make the median 8.

8	
5	
10	
3	
#	

26.	In the list of five measurements shown below, one is blurred.  Supply a fifth value that would make the median 5.

8	
5	
10	
3	
#	

27.	Create a set of five positive numbers that have median 6 and mean 10.	

28.	Create a set of five positive numbers that have median 8 and mean 6.	

29.	Below is a list of gas mileage ratings for selected passenger cars in miles per gallon:
 
 53, 43, 89, 41, 85, 86, 91, 92, 95, 94, 86, 102, 114, 30, 123
 
Make a boxplot to represent this data.	

30.	The scores of students on a standardized test form a normal distribution with a mean score of 500 and a standard deviation of 100.  Between what two values do the middle 50% of scores lie? 	

31.	The average length of time, per week, that students at a certain university spend on homework is normally distributed with a mean of 24.3 hours and a standard deviation of 1.4 hours.  Jane tells her parents she spends more time studying than 75% of the students on campus.  How many hours per week must Jane spend on homework for this to be true? 	

32.	The scores of students on a standardized test form a normal distribution with a mean of 300 and a standard deviation of 40.  Two thousand students took the test.  Find the number of students who score above 380. 	

33.	The distribution of the scores on a standardized exam is approximately normal with mean 400 and standard deviation 35. What percentage of scores lie between 435 and 470? 	

34.	The distribution of the scores on a standardized exam is approximately normal with mean 400 and standard deviation 35. Between what two values do the middle 50% of scores lie? 	

Answer Key

1.	
	
2.	0|001122234567	
3.	

The distribution is not quite symmetric.	
4.	 
	
5.	The median score is 73.	
6.	The median income is $25,000.	
7.	The mean is 27.56.	
8.	The mean age is 14.11 years.	
9.	The first quartile is 13 years.  The third quartile is 16 years.	
10.	The five-number summary is:  37, 58, 73, 81.5, 98.	
11.	The five-number summary is:  1, 2, 9, 15, 18.	
12.	
	
13.	
	
14.	The variance is 1269.33.	
15.	The variance is 40.	
16.	In town A, the mean income is $30,000 and almost all residents earn between $20,000 and $40,000.  The standard deviation of $2600 says incomes do not vary much among residents of the town.  In town B, since the standard deviation is $25,000, we know that there are very poor residents and very rich residents even though the mean income is also $30,000.	
17.	The standard deviation is 6.32.	
18.	The standard deviation is 6.23.	
19.	The variance and standard deviation are both 1.	
20.	If the variance is less than one, then the standard deviation will also be less than one and larger than the variance.	
21.	Yes, the advertisement could be true.  The presence of a car or cars with a sale price of $200 (the outlier(s) on the histogram) could lower the mean sale price to $12,000.	
22.	Since the distribution is skewed, the five-number summary would be the better choice to describe the data shown in the histogram.	
23.	The missing number must be 9.	
24.	The missing number must be 4.	
25.	Answers may vary.  Any value greater than or equal to 8 would be correct.	
26.	Answers may vary.  Any value less than or equal to 5 would be correct.	
27.	Answers may vary. One possibility is {2, 2, 6, 20, 20}.	
28.	Answers may vary.  One possibility is {3, 3, 8, 8, 8}.	
29.	
	
30.	The middle 50% of all scores lie between 433 and 567.	
31.	Jane must study more than 25 1/4 hours.	
32.	50	
33.	13.5%	
34.	Between 377 and 423