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!
9. 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
12. 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
13. 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
15. 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
16. 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
18. 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
21. 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
22. 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
23. 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
24. 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
25. • 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
26. 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)
27. 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
28. Median
• When is median a better indicator of
“average” than the mean?
29. 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
