Assignment: Creating Graphs Review and Practice
Topic: Pie Charts Directions
-used to emphasize each category’s relation to the whole population
-computation requires a conversion from counts to percents to degrees
-use a protractor to measure the degrees or use technology (for example, Excel©)
-label each section with a categorical label and the percentage
Example:
Stuffed Animals
at a Hospital
Type of Animal Frequency
Giraffe
Turtle
Bunny
Puppy
Elephant
Monkey
4
3
10
5
6
2
Step 1: Find the percent of each category and then determine how much of the circle that would
correspond to in the pie chart.
Step 2: Draw the circle with the corresponding sections for each category.
Assignment: Creating Graphs Review and Practice
Topic: Stemplots Directions
-used to visually organize and order a set of data
-requires a stem, leaves, and a key
-once created, the shape or pattern in the data can be described (gaps, clusters, symmetry?)
-order the data, then create a stem by grouping by 10s, 100s, etc., write the remaining parts outwards as
the leaves, finally make a key
Example:
Traffic violations are serious and cause numerous accidents. One insurance agency wants to know
when a particular violation first occurs from their customers. Below are the ages of 26 people at the time
they were first pulled over for failing to stop at a stop sign.
128 122 125 134 137 125 165 118 130 126 128 119 120
121 157 166 151 153 117 125 133 121 122 120 118 127
Step 1: Put the data in order:
117 118 118 119 120 120 121 121 122 122 125 125 125 126 127 128 128 130 133 134
137 151 153 157 165 166
Step 2: Create the stems and then the corresponding last digits as the “leaves.” DO NOT FORGET THE
KEY!
Ages of Drivers Pulled Over
Assignment: Creating Graphs Review and Practice
Topic: **Boxplots** Directions
-commonly used to provide a brief description of the center and spread of data
-divides the data into 25% sections called quartiles
-if you find two middle terms, calculate the average between them.
-order the data, find the median, find the first and third quartile (the medians of the
two halves you created), find the lowest and highest value. Next, graph these points on a number line.
Note: If two numbers are in the “middle,” average them.
25%
25%
25%
25%
Example: The following are the shoe sizes of 15 students in a classroom. Create a boxplot.
8
8.5
6
9
9
8.5
10
12.5
7
5
6
8.5 7 7.5 6.5
Step 1: Put the data in order and find the middle number (median)
5
6
6
6.5
7
7
7.5
8 8.5 8.5
Median = 8
8.5
9
9
10
12.5
Step 2: Find the middle of the upper half (3rd Quartile) and the middle of the lower half (1st quartile).
5
6
6
6.5 7 7 7.5 8 8.5 8.5 8.5 9 9 10
First Quartile = 6.5
Third Quartile = 9
12.5
Step 3: Plot the minimum, 1st quartile, median, 3rd quartile, and maximum above a number line.
Shoe Size of Students in a Classroom
Assignment: Creating Graphs Review and Practice
Topic: Histograms Directions
-commonly used graph to describe the shape of a distribution, especially to check normality
-separates the data into intervals, then displays a frequency for each interval.
-histograms require at least 5 intervals
-order the data, create intervals that section the data, count how many observed values fall within the
interval, then graph the intervals along the x-axis and the frequencies along the y-axis
Example:
A new golf course petitioned the PGA for inclusion in next year’s competitions. Before the PGA will
accept the golf course, they asked 27 professional golfers to test the course and report their total
strokes. If the golfers’ scores were too far below par (72) they would have to deny the petition.
68
81
75
70
77
77
78
68
67
66
70
65
69
70
67
71
69
82
71
71
70
70
72
65
74
73
68
Step 1: Determine appropriate intervals and count the frequency a value falls
in the interval.
Intervals
Frequency
65 – 67
5
68 – 70
10
71 – 73
5
74 – 76
2
77 – 79
3
80 – 83
2
Step 2: Create a bar that corresponds to each interval and the height corresponds to the frequency.
Assignment: Creating Graphs Review and Practice
Topic: Relative Cumulative Frequency Graphs (Ogive) Directions
-used to describe the relative standing of an individual compared to the population
-converts the frequencies into percentages (showing percentiles)
-order the data, create intervals that section the data (at least 5), count how many observed values fall
within the interval, calculate the relative frequencies, then the cumulative relative frequencies, finally
graph the intervals along the x-axis and the cumulative relative frequencies along the y-axis
Example: The expected age of teachers is said to be getting younger. Using the following data,
construct a relative cumulative frequency graph. Would a teacher at the age of 27 be unusually young?
Teacher’s
Frequency
Age
20-24
9
25-29
12
30-34
13
35-39
7
40-44
4
45-49
5
50-54
3
55-59
1
Step 1: Determine the relative frequency (frequency/total) for each interval. Also calculate the
cumulative frequency for each interval and then the relative cumulative frequency for each.
Relative
Teacher’s
Relative
Cumulative
Frequency
Cumulative
Age
Frequency Frequency
Frequency
20-24
9
9/54 = .1667
9
.1667
25-29
12
12/54 = .2222
21
.3889
30-34
13
13/54 = .2407
34
.6296
35-39
7
7/54 = .1296
41
.7592
40-44
4
4/54 = .0741
45
.8333
45-49
5
5/54 = .0926
50
.9259
50-54
3
3/54 = .0556
53
.9815
55-59
1
1/54 = .0185
54
1.0
Step 2: Plot the interval start vs. the relative cumulative frequency.
Rel. Cumul. Freq. (%)
Teacher's Ages in an Area
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
< 20
< 25
< 30
< 35
< 40
< 45
Age Group (years)
< 50
< 55
< 60
Assignment: Creating Graphs Review and Practice
Practice Problems:
Pie charts:
1. The table below shows the number of items sold at a local drive-thru. Create a pie chart for the sales
percentages.
2. Diego loves to play video games. His parents added a feature to his gaming system that tracks to total time
on each game and sends them an email every week. In the past week he played a total of 470 minutes. The
email reported that Call of Duty was played 180 minutes, Halo was played 40 minutes, 38 minutes were
used on Lego Indiana Jones, EA Sports NCAA Football was played 94 minutes, God of War was played 27
minutes, and Rock Bank was played 91 minutes. Create a pie chart.
Stem plots:
3. A male Giant Panda can weigh up to 330 lbs. Below are the weights of 18 Giant Pandas, found in zoos
throughout the world. Create a stemplot of this data.
284
288
292
296
275
330
314
334
307
306
285
289
295
279
281
299
327
311
4. Of the 50 species of oaks in the United States, 28 grow on the Atlantic coast and 11 grow in California. We
are interested in the distribution of acorn sizes among oak species. Here are data on the volumes of acorns
(in cubic centimeters) for these 39 oak species:
Atlantic
1.4
6.8
0.6
3.6
3.4
1.8
1.8
8.1
9.1
0.3
4.8
3.6
1.6
0.9
1.1
1.8
California
1.5
0.8
3.0
0.4
2.5
2.0
1.1
1.1
0.9
1.1
1.1
1.2
4.1
1.6
2.0
5.5
5.9
2.6
6.0
1.0
7.1
0.4
7.1
Make back to back stemplots for the two regions of the United States.
Box Plots:
5. Below are 20 scores from a previous exam. Create a boxplot.
71
53
67
65
100
83
69
65
51
75
68
75
66
77
61
61
72
64
68
74
6. The number of Facebook friends can vary a lot from person to person. Below are numbers from several
students. Create a boxplot.
235
370
316
296
404
352
337
382
425
Assignment: Creating Graphs Review and Practice
Histograms:
7. The number of unprovoked attacks by alligators is sore issue for the Florida Tourism Department. Below
are the numbers for a 33-year period. Create a histogram of the number of unprovoked attacks.
8. The pulse rates for 22 track athletes are given below. Create a histogram for the pulse rate. A recommended
interval would be 10 beats per minute. Create a histogram.
104
101
94
72
100
80
69
55
93
71
75
64
96
88
70
103
69
68
67
95
59
62
Cumulative Relative Frequency (Ogive):
9. The following are scores from an arithmetic test administered to 21 eighth-graders. Create a relative
cumulative frequency graph from this data.
6
23
16
13
24
25
18
21
28
14
13
21
8
19
15
2
11
17
22
11
17
10. The following is IQ scores for 30 randomly chosen fifth-grade students. Create a relative cumulative
frequency graph from this data.
145
112
127
139
109
124
126
134
122
113
125
81
130
113
96
123
110
94
118
100
118
136
101
109
142
131
134
117
124
110