Transcript Chapter 2-5: Statistic Displaying and Analyzing Data

Statistics - Displaying and Analyzing Data
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Statistics - Displaying and Analyzing Data
How many people do you know with the same first name?
Some names are more popular than others. The table lists the top
five most popular names for boys and girls born in each decade
from 1950 to 1999.
Statistics - Displaying and Analyzing Data
To help determine which names appear most
frequently, these data could be displayed graphically.
In some cases, data can be presented using a line plot.
Most line plots have a number line labeled with a scale
to include all the data.
Then an × is placed above a data point each time it
occurs to represent the frequency of the data.
Create a Line Plot
Draw a line plot for the data.
11 –2 10 –2 7 2 7 4 9 0 6 9 7 2 0 4 10 7 6 9
Step 1
The values of the data range from –2 to 11, so
construct a number line containing these values.
Step 2
Then place an  a number for each
time it occurs.
Create a Line Plot
Draw a line plot for the data.
3 5 7 6 0 –4 6 4 7 0 0 –2 3 7
Answer:
Line plots are a convenient way to organize data
for comparison.
Use a Line Plot to Solve a Problem
Traffic The highway patrol did a radar survey of the
speeds of cars along a stretch of highway for 1
minute. The speeds (in miles per hour) of the 20
cars that passed are listed below.
72 70 72 74 68 69 70 72 74 75
79 75 74 72 70 64 69 66 68 67
Make a line plot of the data.
The lowest value is 64 and the highest value is 79, so use
a scale that includes those values. Place an  above each
value for each occurrence.
Use a Line Plot to Solve a Problem
Answer:
Use a Line Plot to Solve a Problem
Which speed occurs the most frequently?
Answer: Looking at the line plot, we can easily see that
72 miles per hour occurs most frequently.
Use a Line Plot to Solve a Problem
Family Size Students in Mrs. Barrett’s class listed the
number of family members in their households below.
6 4 8 3 3 5 4 4 3 5 5 2 5 6 3 5 6 2 4 4 4
a. Make a line plot of the data.
Answer:
b. Which family size occurs the most frequently?
Answer: 4
Statistics - Displaying and Analyzing Data
greatest common place value is used for the stems.
The numbers in the next greatest place value are used
Another
wayleaves.
to organize data is by using a stem-and-leaf p
to form the
In a stem-and-leaf plot, the
Create a Stem-and-Leaf Plot
Use the data below to make a stem-and-leaf plot.
85 115 126 92 104 107 78
85 116 100 121 123 131 88
79 90 110 129 108 93 84
131 114 92
97 99 116
75 70 132
The greatest common place value is tens, so the digits in
the tens place are the stems.
Create a Stem-and-Leaf Plot
Answer:
Stem
7
8
9
10
11
12
13
Leaf
0589
4558
022379
0478
04566
1369
112
A key is included to indicate
what the stems and leaves
represent when read
The leaves are in
numerical order.
Create a Stem-and-Leaf Plot
Use the data below to make a stem-and-leaf plot.
3 5
13 25
Answer:
7
32
11
37
Stem
0
1
2
3
10
21
15
10
21
12
11
Leaf
357
0011235
115
27
A back-to-back stem-and-leaf plot can be used to
compare two related sets of data.
Back-to-Back Stem-and-Leaf Plot
Weather Monique wants to compare the monthly
average high temperatures of Dallas and Atlanta
before she decides to which city she wants to move.
The table shows the monthly high temperatures (F)
for both cities.
54
83
87
Monthly Average
High Temperature
Dallas
Atlanta
59 68 77
50 55 64
91 95 95
75 85 88
78 66 57
81 72 63
72
87
54
Back-to-Back Stem-and-Leaf Plot
Make a stem-and-leaf plot to compare the data.
To compare the data we can use a back-to-back stemand-leaf plot. Since the data represent similar
measurements, the plot will share a common stem.
Answer: Dallas
9 7
8
8
7
5 5
4
6
7
3
1
Stem
5
6
7
8
9
Atlanta
0 4 5
3 4
2 2 5
1 5 7 8
Back-to-Back Stem-and-Leaf Plot
What is the difference between the highest average
temperatures in each city?
Answer: 95 – 88 or 7°
Dallas
9 7 4
8 6
8 7
7 3
5 5 1
Stem
5
6
7
8
9
Atlanta
0 4 5
3 4
2 2 5
1 5 7 8
Back-to-Back Stem-and-Leaf Plot
Which city has higher average temperatures?
Answer: Looking at the temperatures of 80 and above,
we can see that Dallas has a higher number of average
temperatures above 80°.
Dallas
9 7 4
8 6
8 7
7 3
5 5 1
Stem
5
6
7
8
9
Atlanta
0 4 5
3 4
2 2 5
1 5 7 8
Back-to-Back Stem-and-Leaf Plot
Ms. Smith wants to compare the final grades for
two of her classes. The table shows the scores for
both classes.
Class A
87
96
81
51
99
62
76
57
92
76
71
77
72
69
83
85
91
98
75
64
Class B
Back-to-Back Stem-and-Leaf Plot
a. Make a back-to-back stem-and-leaf plot to compare
the data.
Answer: Class A
1
4
6 5 1
7 1
8 6 2
Stem
5
6
7
8
9
Class B
7
2 9
2 6 7
3 5
1 9
Back-to-Back Stem-and-Leaf Plot
b. What is the difference between the highest score
in each class?
Class A
Answer: 1 point
1
4
6 5 1
c. Which class scored higher
7 1
overall for the grading period?
8 6 2
Answer: Class A
Stem
5
6
7
8
9
Class B
7
2 9
2 6 7
3 5
1 9
Statistics - Displaying and Analyzing Data
When analyzing data, it is helpful to have one number
that describes the set of data.
Numbers known as measures of central tendency are
often used to describe sets of data because they
represent a centralized, or middle value.
Three of the most commonly used measures of
central tendency are the mean, median and mode.
Statistics - Displaying and Analyzing Data
When you use a measure of central tendency to
describe a set of data, it is important that the measure
you use best represents all of the data.
Extremely high or low values can affect the mean,
while not affecting the median or mode.
A value with a high frequency can cause the mode to
be misleading.
Data that is clustered with a few values separate from
the cluster can cause the median to be too low or too
high.
Analyze Data
Which measure of central tendency best
represents the data?
Determine the mean, median, and mode.
Stem Leaf
4
5
6
7
8
11244458
0
257
39
1
The mean is about 5.5.
Add the data and divide by 15.
The median is 4.8.
The middle value is 4.8
The mode is 4.4.
The most frequent value is 4.4.
Analyze Data
The mean is about 5.5.
The median is 4.8.
The mode is 4.4.
Stem
4
5
6
7
8
Leaf
11244458
0
257
39
1
Answer: Either the median or the mode best represent
the set of data since both measures are located in the
center of the majority of the data. In this instance, the
mean is too high.
Analyze Data
Which measure of central tendency best
represents the data?
Stem
1
2
3
4
5
Leaf
011568
378
2
6
459
Answer: The mean is about 2.9. The median is 2.5. The
mode is 1.1. Either the mean or median can be used to
represent the data. The mode is too low.
Determine the Best Measures of Central Tendency
Politics The number of electoral college votes for the
12 most populous states in the 2000 Presidential
election are listed below. Which measure of central
tendency best represents the data?
21
14
22
32
18
13
23
15
25
33
13
54
The mean is about 23.6. Add the data and divide by 12.
The median is 21.5.
The middle value is 21.5.
The mode is 13.
The most frequent value is 13.
Answer: Either the mean or median can be used to best
represent the data. The mode is too low.
Determine the Best Measures of Central Tendency
The number of points scored by the basketball team
during each game in the season is listed below. Which
measure of central tendency best represents the data?
48
51
45
81
52
62
63
73
59
68
64
82
67
73
72
70
58
65
Answer: Either the mean or the median can be used to
best represent the data. The mode is too high.