lecture 10.1 10.2 bt
TRANSCRIPT
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Today’s Agenda
Attendance / AnnouncementsCollect Projects
Note about Final Exam
Return Exams
Remaining Schedule
Sections 10.1, 10.2
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Exam Schedule
Exam 5 (Ch 10)
Thur 12/5
Final Exam (All)
Thur 12/12
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Intro to Statistics
Statistics is the science that deals with the collection and summarization of data. Methods of stat analysis allow us to make conclusions about a population based on sampling.
Statistics is more a field of
Communications, than one of
Mathematics!
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Intro to Statistics
1. Organize Data
2. Display Data
3. Identify the “averages” of the data
4. Identify the “spread” of the data
5. Make conclusions
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Obtaining Data
• Want to represent a Population
• Collect data from a Sample
–Should be a Random Sample to be
a fair representation of the
population
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Tuition for a random sample of 30
private, 4-year colleges(thousands)
23 22 38 25 11 16
15 26 23 24 37 18
21 36 36 28 18 9
39 17 27 24 10 32
24 27 22 24 28 39
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23 22 38 25 11 16
15 26 23 24 37 18
21 36 36 28 18 9
39 17 27 24 10 32
24 27 22 24 28 39
There are 30 Data Items, so n = 30
Where each can be called
So,
“21”, “37”, etc. are Data Values
ix254x
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Organizing Data
• Frequency Distribution Table– Organize data into Classes
• Usually between 5 - 15
– Each class must have the same Class Width
Class width* = Max data value – Min data value
Number of classes
*Round up to nearest integer
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Organizing Data
Let’s make a Freq. Dist. Table with 7 classes to organize
the tuition data…Need Class Width!
28.47
939*CW
So, each class will have a class width of 5!
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Organizing Data
Note: Class width is not (9 – 5)!!!
It is the distance between the lower
limit of each class.
Make
this
column
first!
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Displaying Data1. An account ing firm selected 24 complex tax returns prepared by a certa in tax preparer. The number of
errors per return were as follows. Group the data into 5 classes, and make a frequency table and
histogram/ polygon to represent the data.
Your Class Width =
8 12 0 6 10 8 0 14
8 12 14 16 4 14 7 11
9 12 7 15 11 21 22 19
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Displaying Data
• Frequency Histogram (bar graph)–Each class is its own “bar”
• No spaces between classes (bars)
–Must label each axis (classes vs. frequency)
–Use straightedge to make lines
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1
3
4
5
6
7
8
9
2
freq
uen
cy
Tuition
5-9
10
-14
15-1
9
20
-24
25-2
9
30-3
4
35-3
9
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Displaying Data
• Frequency Polygon (line graph)
–Connects the midpoints of the top of each class.
–Then connect to ground on each side
–Use straightedge to make lines
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1
3
4
5
6
7
8
9
2
freq
uen
cy
Tuition
5-9
10
-14
15-1
9
20
-24
25-2
9
30-3
4
35-3
9
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Characterizing Data
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Displaying Data1. An account ing firm selected 24 complex tax returns prepared by a certa in tax preparer. The number of
errors per return were as follows. Group the data into 5 classes, and make a frequency table and
histogram/ polygon to represent the data.
Your Class Width =
8 12 0 6 10 8 0 14
8 12 14 16 4 14 7 11
9 12 7 15 11 21 22 19
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10.2 Measures of Central Tendency
• Ways to describe “on average…”
–Mean
• What is commonly thought of as
“average”
–Median
• The “middle” of the data
–Mode
• The data value that occurs most often
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We need some data…
• Number of hits during spring training for 15
Phillies players: (alphabetical order)
21 19 10 1 6
28 32 11 2 15
2 17 21 29 21
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Sample Mean
n
xx
• The mean of a sample set of data
“x bar” is the
sample mean.
Round to
nearest
hundredth. (2
decimal places)
The sum of all
data values
The number of
data items
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• Number of hits for 15 Phillies players:
21 19 10 1 6
28 32 11 2 15
2 17 21 29 21
67.1515
211921
n
xx
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Median
• The “middle” of an ordered data set
– Arrange data in order
– Find middle value
• If n is odd, simply select middle value as the
median.
• If n is even, the median value will be the
mean of the two central values (since a
“middle” does not exist)
2
1nposition
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Median
Find the median for each data set.
Age (years) in the intensive care unit at a local hospital.
68, 64, 3, 68, 70, 72, 72, 68
Starting teaching salaries (U.S. dollars).
$38,400, $39,720, $28,458, $29,679, $33,679
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Median
• When is median a better indicator of
“average” than the mean?
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Mode
• The data value that appears most often
– Single Mode
• One data value appears more than any other
– No Mode
• No data values repeat
– Multi-Mode
• There is a “tie” for the value that appears the most
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Mode
• Mode of Phillies data?
• 2, 3, 3, 3, 5, 6, 6, 6, 7, 7, 10
• 18, 34, 61, 62, 85
• 9.5, 9.2, 9, 9, 9.1, 8.9
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Classwork / Homework
• Page 604
•1, 7, 21 – 25
• Page 614
•1 – 19 odd, 29