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Today’s Agenda
Attendance / AnnouncementsCollect Projects
Note about Final Exam
Return Exams
Remaining Schedule
Sections 10.1, 10.2
Exam Schedule
Exam 5 (Ch 10)
Thur 12/5
Final Exam (All)
Thur 12/12
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!
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
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
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
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
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
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!
Organizing Data
Note: Class width is not (9 – 5)!!!
It is the distance between the lower
limit of each class.
Make
this
column
first!
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
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
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
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
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
Characterizing Data
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
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
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
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
• 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
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
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
Median
• When is median a better indicator of
“average” than the mean?
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
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
Classwork / Homework
• Page 604
•1, 7, 21 – 25
• Page 614
•1 – 19 odd, 29