Section 3.
2 Solutions
Homework #1-4
1) Create a frequency histogram and a frequency polygon from the data in the frequency distribution
below.
I will put the numbers in the left column along the “x-axis”.
I incremented my y-axis by 5 as it made it less messy.
I made bars of the appropriate height for my frequency histogram.
I put points at the correct height and connected them with line segments for my polygon.
Frequency Histogram
20
number of families
15
10
5
0
0 1 2 3 4 5 6 7 8 9
Number of Children
Frequency polygon
20
Number of families
15
10
5
0
0 1 2 3 4 5 6 7 8 9
Number of children
3) Create a frequency histogram and a frequency polygon from the data in the frequency distribution
below. Put the entire class on the horizontal axis.
I will put the entire range of
numbers in the left column along the “x-axis”.
I incremented my y-axis by 5 as it made it less messy.
I made bars of the appropriate height for my frequency histogram.
I put points at the correct height and connected them with line segments for my polygon.
Histogram
20
Number of families
15
10
5
0
Income in thousands of dollars
Frequency polygon
20
Number of families
15
10
5
0
16-22 23-29 30-36 37-43 44-50 Total
Income in thousands of dollars
Homework #5-8: Create a stem and leaf display for the given data.
5) The table below indicates the ages of each student in a recent MAT 142 class. Construct a stem and
leaf display.
18 18 18 19 19
20 20 21 25 28
31 35 36 44 49
The left column will have the numbers 1,2,3,4. I put ones part of each number next to the appropriate
stem.
Stem Leaves
1 8889
2 00158
3 156
4 49
7) Starting salaries of recent computer science majors (in thousands of dollars) are given in the table
below. Construct a stem and leaf display.
42 45 48 49 50 51
55 57 58 59 60 61
62 64 65 66 67 73
The left column will have the numbers 4,5,6,7. I put ones part of each number next to the appropriate
stem.
Stem Leaves
4 2589
5 015789
6 0124567
7 3
Homework #9-11: Construct a Circle graph from the given data.
9) I need to attach a percent to each number. I just divide each number in the right column by the total
of the right column. This gives a decimal. I then change that decimal to a percent.
Type of cell phone Number of users
IPhone 50 (50/100 = 0.50 = 50%)
Galaxy 25 (25/100) = 0.25 = 50%)
Flip Phone 10 (10/100 = 0.10 = 10%)
Other 10 (10/100 = 0.10 = 10%)
No cell phone 5 (5/100 = 0.05 = 5%)
5%
10%
10%
50%
25%
IPhone Galaxy Flip Phone Other No cell phone
11) I need to attach a percent to each number. I just divide each number in the right column by the
total of the right column. This gives a decimal. I then change that decimal to a percent.
Height Number of people
5 feet – 5 feet 6 inches 100 (100 / 200 = 0.50 = 50%)
5 feet 7 inches to 6 feet 80 (80/200 = 0.40 = 40%)
Over 6 feet 1 inch 20 (20/200 = 0.10 = 10%)
10%
50%
40%
5 feet – 5 feet 6 inches 5 feet 7 inches to 6 feet
Over 6 feet 1 inch
Homework: 12 - 19
13) A survey was given to 500 students. The results are summarized in the circle graph below.
a) How many students favorite type of music is country? 500*.03 = 15
b) What is the most popular type of music and how many students say it is their favorite?
Pop, 500*0.64 = 320
15) 300 people attended a concert. The circle graph below summarizes the ages of the people who
attended the concert.
a) How many people at the concert were 30 or older?
I need to find the percent to multiply. This question includes the 30-39 group, 40-49 and greater than or
equal to 50 group.
31% + 25% + 10% = 66%
.66*300 = 198
Answer: 198 people
b) How many were under 50?
10% of the people are over 50. Hence, 90% are under 50.
0.90*300 = 270
Answer: 270 people
17) The ages of people attending a school assembly are summarized in the histogram below. You will
have to estimate some of the numbers, and your answer could be slightly different than mine if your
estimates are different.
Chart Title
90
80
number of students
70
60
50
40
30
20
10
0
8 9 10 11 12 13 14 15 16 17
age in years
a) How many people were at least 15?
Add up the heights of the 15, 16 and 17 bars.
40 + 20 + 10
Answer: 70
b) How many were under 12?
Add up the heights of the 8, 9, 10 and 11 bars. Don’t include the 12 as the requirement is to be under
12.
10 + 20 + 40 + 60 = 130
Answer: 130
19) 300 men were measured. The results (in percent) are summarized in the histogram below.
20
18
16
Number with the height
14
12
10
8
6
4
2
0
63 64 65 66 67 68 69 70 71 72 73 74
Height in inches
a) How many men had heights between 68 and 70 inches inclusive?
Add up the heights of the 68, 69 and 70 bars.
10 + 12 +15 = 37
Answer: 37 men
b) What percent of the men had heights greater than 72 inches?
Add up the heights of the 73 and 74 bars.
4+3 =7
Answer: 7 men
