MATH 106 6383 Finite Mathematics (2192)
Week 6 Discussion
INTRODUCTION TO STATISTICS
(Online Statistics Education: A Multimedia Course of Study, Chapter 1: “Distributions” ; Chapter 2 “Histograms” ; Chapter 3 “Measures of Central Tendency” and “Measures of Variability”; Chapter 5 “Binomial Distribution”)
CHARTS, FREQUENCY TABLES, HISTOGRAMS
The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. The following table shows the four seasons,the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct abar graph showing the number of students.
Seasons
Number of students
Proportion of Population
Spring
8
24%
Summer
9
26%
Fall
11
32%
Winter
6
18%
A student has decided to display the results of his project on the number of hours people in various countries slept per night. He compared the sleeping patterns of people from the US, Brazil, France, Turkey, China, Egypt, Canada, Norway, and Spain. He was planning on using a line graph to display
this data. Is a line graph appropriate? What might be a better choice for a graph?
For the data in the table below from the 1977 University of New Hampshire Stat. and Biom. 200 class for eye color, construct a pie graph:
Eye Color
Brown
Blue
Green
Gray
Number of Students
11
10
4
1
(Question submitted by J. Warren, UNH)
For the data in the table below from the 1977 University of New Hampshire Stat. and Biom. 200 class for eye color, construct a horizontal bar graph:
Eye Color
Brown
Blue
Green
Gray
Number of Students
11
10
4
1
(Question submitted by J. Warren, UNH)
For the data in the table below from the 1977 University of New Hampshire Stat. and Biom. 200 class for eye color, construct a vertical bar graph:
Eye Color
Brown
Blue
Green
Gray
Number of Students
11
10
4
1
(Question submitted by J. Warren, UNH)
Using the data below, complete the frequency table.
DATA: 30, 32, 11, 14, 40, 37, 16, 26, 12, 33, 13, 19, 38, 12, 28, 15, 39, 11, 37, 17, 27, 14, 36
Interval
Frequency
11 – 15
16 – 20
21 – 25
26 – 30
31 – 35
36 – 40
Twenty five applicants to the Peace Corps are given a blood test to determine their blood type. The data set is:
A B B AB O
O O B AB B
B B O A O
A O O O AB
AB A O B A
Complete the following frequency distribution and construct a bar chart for this data.
Blood Types
Frequency
A
B
O
AB
Total
The test scores for 10 students in Ms. Sampson’shomeroom were 61, 67, 81, 83, 87, 88, 89, 90,98, and 100. Complete the frequency table.
Interval
Frequency
61 – 70
71 – 80
81 – 90
91 – 100
The scores on a mathematics test were 70, 55, 61, 80, 85, 72, 65, 40, 74, 68, and 84. Completethe accompanying table, and use the table to construct a frequency histogram for these scores.
Interval
Frequency
40 – 49
50 – 59
60 – 69
70 – 79
80 – 89
Create a frequency table and histogram using the given information.
Number of crimes committed in 1984 in Metropolisburg:
January
124
February
96
March
89
April
113
May
107
June
102
July
85
August
87
September
91
October
119
November
122
December
115
Interval
Frequency
80 – 89
90 – 99
100 – 109
110 – 119
120 – 129
The following data consists of the weights, in pounds, of 24 high school students: 195, 206, 100, 98, 150, 210, 195, 106, 195, 108, 180, 212, 104, 195, 100, 216, 99, 206, 116, 142, 100, 135, 98, 160. Using this data, complete the accompanying frequency table and construct a frequency histogram for this data.
Interval
Frequency
51 – 100
101 – 150
151 – 200
201 – 250
Create a frequency table and histogram using the following scores from a recent high school English test:
81
77
63
92
97
68
72
88
78
96
85
70
66
95
80
99
63
58
83
93
75
89
94
92
85
76
90
87
Interval
Frequency
51 – 60
61 – 70
71 – 80
81 – 90
91 – 100
In a histogram, when the data are skewed left, what is the typical relationship between the mean and median?
In a histogram, when the data are symmetrical, what is the typical relationship between the mean and median?
Which of the frequency polygons has a large positive skew? Which has a large negative skew?
MEASURES OF CENTRAL TENDENCY
The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200. For these six salaries, find: (a) the mean (b) the median (c) the mode
Andy has grades of 84, 65, and 76 on three math tests. What grade must he obtain on the next test to have an average of exactly 80 for the four tests?
Test scores for a class of 20 students are as follows:
93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95
Find the mean, mode, median and range for your data.
In January of 2006, your family moved to a tropical climate. For the year that followed, you recorded the number of rainy days that occurred each month. Your data contained 14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13, 8. Find the mean, mode, median and range for your data set of rainy days.
The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest: 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40. Calculate the mean, median, mode(s) (if it/they exist(s)), and range.
Calculate the mean, median, and mode(s) (if it/they exist(s)) for the following data set:
1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3; 4; 4; 4; 5; 5
Calculate the mean, median, and mode(s) (if if/they exist(s)) for the following data set:
16; 17; 19; 22; 22; 22; 22; 22; 23
Calculate the mean, median, and mode(s) (if it/they exist(s)) for the following data set:
87; 87; 87; 87; 87; 88; 89; 89; 90; 91
Twenty-five randomly selected students were asked the number of movies they watched the previous week. The resultsare as follows:
Number of movies
Frequency
0
5
1
9
2
6
3
4
4
1
Find the sample meanx .
MEASURES OF VARIABILITY
The following data are the distances between 20 retail storesand a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
Find the variance and standard deviation (round each to the nearest tenth)
The population of full-time-equivalent students (FTES) at Lake Tahoe Community Collge for 2005–2006 through 2010–2011 was given in an updated report. The data are reported as follows:
Year
2005 – 06
2006 – 07
2007 – 08
2008 – 09
2009 – 10
2010 – 11
FTES
1585
1690
1735
1935
2021
1890
Calculate the mean, variance, and standard deviation. Round to one decimalplace.
The attitudes of a sample of 12 teachers attending a seminar on mathematical problem solving were measured before and after the seminar. A positive number for change in attitude indicates that ateacher’s attitude toward math became more positive. The 12 change scores are as follows:
3; 8; –1; 2; 0; 5; –3; 1; –1; 6; 5; –2
What is the mean change score?
What is the standard deviation for this sample?
Forty randomly selected students were asked the number of pairs of sneakers they owned. LetX= the number of pairsof sneakers owned. The results are as follows:
X
Frequency
1
2
2
5
3
8
4
12
5
12
6
0
7
1
Find the sample meanx .
Find the sample standard deviation,s
Calculate the sample mean, sample variance, and sample standard deviation for the following data set:
2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0
Calculate the sample mean, sample variance, and sample standard deviation for the following data set:
1.112 ; 1.245 ; 1.361 ; 1.372 ; 1.472
Calculate the sample mean, sample variance, and sample standard deviation for the following data set:
3.0 ; 3.4 ; 2.6 ; 3.3 ; 3.5 ; 3.2
BERNOULLI TRIALS AND BINOMIAL DISTRIBUTION(Chapter 5, Section: “Binomial Distributions”
The probability of “heads” coming face-up on a single flip of a fair two-sided coin is 0.5. You flip the coin a total of ten (10) times. What is the probability of getting exactly 7 “heads” in those 10 flips?
The probability that you will win a certain game is 0.3. If you play the game 20 times, what is the probability that you will win at least 8 times?
The probability that you will win a certain game is 0.3. If you play the game 20 times, what is the probability that you will win 3 or fewer times?
The probability that you will win a certain game is 0.3. You play the game 20 times. What are the mean and standard deviation of this binomial distribution?
A biased coin has a .6 chance of coming up heads. You flip it 50 times. What are the mean and standard deviation of this distribution?
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