3.
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!
4.
Intro to Statistics
1.
2.
3.
4.
5.
Organize Data
Display Data
Identify the “averages” of the data
Identify the “spread” of the data
Make conclusions
5.
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
7.
23
15
21
39
24
22
26
36
17
27
38
23
36
27
22
25
24
28
24
24
11
37
18
10
28
16
18
9
32
39
There are 30 Data Items, so n = 30
Where each can be called x i
So, x4 25
“21”, “37”, etc. are Data Values
8.
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
9.
Organizing Data
Let’s make a Freq. Dist. Table with 7 classes to organize
the tuition data…Need Class Width!
39 9
CW *
7
So, each class will have a class width of 5!
4.28
10.
Organizing Data
Make
this
column
first!
Note: Class width is not (9 – 5)!!!
It is the distance between the lower
limit of each class.
11.
Displaying Data
1. An account ing firm select ed 24 complex t ax ret urns prepared by a cert a in t ax preparer. T he number of
errors per ret urn were as follows. Group t he dat a int o 5 classes, and make a frequency t able and
hist ogram/ polygon t o represent t he dat a.
Your Class Widt h =
8
12
0
6
10
8
0
14
8
12
14
16
4
14
7
11
9
12
7
15
11
21
22
19
12.
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
14.
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
17.
Displaying Data
1. An account ing firm select ed 24 complex t ax ret urns prepared by a cert a in t ax preparer. T he number of
errors per ret urn were as follows. Group t he dat a int o 5 classes, and make a frequency t able and
hist ogram/ polygon t o represent t he dat a.
Your Class Widt h =
8
12
0
6
10
8
0
14
8
12
14
16
4
14
7
11
9
12
7
15
11
21
22
19
18.
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
19.
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
20.
Sample Mean
• The mean of a sample set of data
The sum of all
data values
“x bar” is the
sample mean.
Round to
nearest
hundredth. (2
decimal places)
x
x
n
The number of
data items
21.
• Number of hits for 15 Phillies players:
21 19 10 1 6
28 32 11 2 15
2 17 21 29 21
x
x
n
21 19
15
21
15 .67
22.
Median
• The “middle” of an ordered data set
– Arrange data in order
– Find middle value
position
n 1
2
• 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)
23.
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
24.
Median
• When is median a better indicator of
“average” than the mean?
25.
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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