General Statistics
1. Compute the mean, median, and mode for each of the following distributions.
A B C D
3 2 1 2
3 2 3 3
4 2 3 4
6 5 3 4
7 5 5 4
8 7 5 5
10 7 8 7
8 8 8
10 8 8
11 9
11
2. I grew up in a very tiny town in the Midwestern United States. The two had seven streets, and the number of buildings on each street were as follows:
Street Number of Buildings
Main Street 27
Myrtle Street 7
Pine Street 12
Walnut Street 9
1st Avenue 11
2nd Avenue 13
3rd Avenue 3
Use three different methods to find a single number that describes how many buildings there are per street in my home town.
3. Some of the students in Mr. Whimper's math class decide to have a spitball throwing contest, to see who had the best range. Sixteen students participated, and their scores (in feet) were as follows: Andrew, 15; Beth, 12; Colin, 14.8; Derek, 10.3; Elspeth, 15; Fiona, 9.5; Glenn, 3 (he got the giggles); Harris, 8.9; Iggy, 22; Jeanine, 13; Ken, 10.4; Leila, 10.5; Max, 11; Norton, 9.9; Opie, 15; and Penny, 7. What was the median score, and who came closest to it? Which was closer to the mean, the median or the mode?
4. Find the range, variance, and standard deviation for the following sets of values.
(a) 1, 2, 3, 4, 5, 6, 7, 8, 9
(b) 10, 20, 30, 40, 50, 60, 70, 80, 90
(c) -4, -3, -2, -1, 0, 1, 2, 3, 4
(d) .1, .2, .3, .4, .5, .6, .7, .8, .9
(e) Number of years in school:
5
3
4
6
8
---
26
(f) Achievement test scores and Comprehension test scores:
Comprehension test scores
25
37
26
20
19
---
127
Achievement test scores
14
19
13
9
13
---
68
(g) The test scores listed below.
Test Scores 1
133
113
112
95
94
Test Scores 2
105
102
101
92
91
80
Test Scores 3
110
105
100
100
100
100
99
98
Test Scores 4
110
105
105
105
100
95
95
95
90
(h) The four sets of numbers in Problem 1.
(i) The number of buildings in Problem 2.
(j) The spitball distances in Problem 3.
2. Suppose that a test of math anxiety was given to a large group of persons, the scores are assumed to be from a normally distributed population, that M = 50 and s = 10. Approximately what percentage of persons earned scores:
1. below 50?
2. above 60?
3. below 30?
4. above 80?
5. between 40 and 60?
6. between 30 and 70?
7. between 60 and 70?
8. below 70?
9. below 80?
10. A major pharmaceutical company has published data on effective dosages for their new product, FeelWell. It recommends that patients be given the minimum effective dose of FeelWell, and reports that the mean effective minimum dose is 250 mg, with a standard deviation of 75 mg (dosage effectiveness is reported to be normally distributed). What dose level will be effective for all but 2% of the total population? What dose level can be expected to be too low for all but 2%?
11. Dennis the Druggie has decided to grow marijuana in his basement. He has learned from friends (who wish to remain nameless) that the average marijuana plant grows to a height of 5'4", with a standard deviation of 8". Within what range can he expect 2/3 of his plants to grow? (Hint: Convert everything to inches, and then convert back to feet when you're done.)
12. New American cars cost an average of $17,500, with s = $2000. If I'm willing to spend up to $15,500, and if car prices are normally distributed, what percentage of the total number of new cars will fall within my budget?
13. Long-distance runners seem to be setting new records every year. If the current mean time for college athletes running the mile is 4 minutes and 32 seconds, with a standard deviation of 1 minute, figure out what the top 2% of runners can be expected to do. If your answer seems unreasonable to you (and it should), how do you explain what happened?
14. According to a survey carried out by the psychology department, students at the University of Oregon drink an average of 3.5 cups of coffee daily (s = 1.2). Assuming that coffee consumption is normally distributed, what percentage of students drink between 3.5 and 5.9 cups a day?
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Solution Summary
1. Compute the mean, median, and mode for each of the following distributions.
A B C D
3 2 1 2
3 2 3 3
4 2 3 4
6 5 3 4
7 5 5 4
8 7 5 5
10 7 8 7
8 8 8
10 8 8
11 9
11
2. I grew up in a very tiny town in the Midwestern United States. The two had seven streets, and the number of buildings on each street were as follows:
Street Number of Buildings
Main Street 27
Myrtle Street 7
Pine Street 12
Walnut Street 9
1st Avenue 11
2nd Avenue 13
3rd Avenue 3
Use three different methods to find a single number that describes how many buildings there are per street in my home town.
3. Some of the students in Mr. Whimper's math class decide to have a spitball throwing contest, to see who had the best range. Sixteen students participated, and their scores (in feet) were as follows: Andrew, 15; Beth, 12; Colin, 14.8; Derek, 10.3; Elspeth, 15; Fiona, 9.5; Glenn, 3 (he got the giggles); Harris, 8.9; Iggy, 22; Jeanine, 13; Ken, 10.4; Leila, 10.5; Max, 11; Norton, 9.9; Opie, 15; and Penny, 7. What was the median score, and who came closest to it? Which was closer to the mean, the median or the mode?
4. Find the range, variance, and standard deviation for the following sets of values.
(a) 1, 2, 3, 4, 5, 6, 7, 8, 9
(b) 10, 20, 30, 40, 50, 60, 70, 80, 90
(c) -4, -3, -2, -1, 0, 1, 2, 3, 4
(d) .1, .2, .3, .4, .5, .6, .7, .8, .9
(e) Number of years in school:
5
3
4
6
8
---
26
(f) Achievement test scores and Comprehension test scores:
Comprehension test scores
25
37
26
20
19
---
127
Achievement test scores
14
19
13
9
13
---
68
(g) The test scores listed below.
Test Scores 1
133
113
112
95
94
Test Scores 2
105
102
101
92
91
80
Test Scores 3
110
105
100
100
100
100
99
98
Test Scores 4
110
105
105
105
100
95
95
95
90
(h) The four sets of numbers in Problem 1.
(i) The number of buildings in Problem 2.
(j) The spitball distances in Problem 3.
2. Suppose that a test of math anxiety was given to a large group of persons, the scores are assumed to be from a normally distributed population, that M = 50 and s = 10. Approximately what percentage of persons earned scores:
1. below 50?
2. above 60?
3. below 30?
4. above 80?
5. between 40 and 60?
6. between 30 and 70?
7. between 60 and 70?
8. below 70?
9. below 80?
10. A major pharmaceutical company has published data on effective dosages for their new product, FeelWell. It recommends that patients be given the minimum effective dose of FeelWell, and reports that the mean effective minimum dose is 250 mg, with a standard deviation of 75 mg (dosage effectiveness is reported to be normally distributed). What dose level will be effective for all but 2% of the total population? What dose level can be expected to be too low for all but 2%?
11. Dennis the Druggie has decided to grow marijuana in his basement. He has learned from friends (who wish to remain nameless) that the average marijuana plant grows to a height of 5'4", with a standard deviation of 8". Within what range can he expect 2/3 of his plants to grow? (Hint: Convert everything to inches, and then convert back to feet when you're done.)
12. New American cars cost an average of $17,500, with s = $2000. If I'm willing to spend up to $15,500, and if car prices are normally distributed, what percentage of the total number of new cars will fall within my budget?
13. Long-distance runners seem to be setting new records every year. If the current mean time for college athletes running the mile is 4 minutes and 32 seconds, with a standard deviation of 1 minute, figure out what the top 2% of runners can be expected to do. If your answer seems unreasonable to you (and it should), how do you explain what happened?
14. According to a survey carried out by the psychology department, students at the University of Oregon drink an average of 3.5 cups of coffee daily (s = 1.2). Assuming that coffee consumption is normally distributed, what percentage of students drink between 3.5 and 5.9 cups a day?