IBS
Statistics
Year
1
What we are going to learn?
Review
Chapter
3-A: Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a.
Mean
b. Mode
c.
Median
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Review
What is the level of measurement for these items related to the newspaper business?
The number of papers sold each Sunday during 2006.
The departments, such as editorial, advertising , sports, etc.
A summary of the number of papers sold by county.
The number of years with the paper for each employee.
P14.
Ratio
Nominal
Ordinal
Interval
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Review
For the follow questions, would you collect information using a sample or a population?
Statistics 201 is a course taught at a university. Professor A has taught nearly 1,500 students in the course over the past 5 years. You would like to know the average grade for the course
You are looking forward to graduation project and your first job as a salesperson for one of five large corporations. Planning for your interviews, you will need to know about each company’s mission, profitability, products, and markets.
P16.
Sample
Population
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Review
-Qualitative Data
Bar Chart
Pie Chart
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Histogram
Polygon
Cumulative Frequency
Distribution
Review
-Quantitative Data
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
Data
a
.
Mean
b
. Mode
c
.
Median
Cumulative Frequency
Distribution
Review
-Quantitative Data
A (21, 30)
Around
_______of the
vehicles
were
seld
below
$21,000.
A
a. 30% b. 43% c. 35 d. 43
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Review
P34.
A set of data
contains
53
observations
. The
lowest
value
is 43 and the
largest
is 129. The data are to
be
organized
into
a
frequency
distribution.
a.
How
many
classes
would
you
suggest
?
2
5
= 32, 2
6
= 64, suggests 6 classes
Use interval of 15
And start first class at 40
b.
What
would
you
suggest
as
class
interval
&
the
lower
limit
of the
first
class
?
a. 4 b. 5 c. 6 d. 7
a. 10 b. 15 c. 18 d. 20
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
Parameter:
a numerical characteristic of a population.
Example:
The fraction of U. S. voters who support Sen. McCain for President is a parameter.
Statistic:
A statistic is a numerical characteristic of a sample.
Example:
If we select a simple random sample of n = 1067 voters from the population of all U. S. voters, the fraction of people in the sample who support Sen. McCain is a statistic.
Review
Chapter
3-A:
Central
Tendency
A.
Grouped
Data
a.
Mean
b. Mode
c.
Median
B.
Ungrouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
Parameter
&
Statistics
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mean
Example:
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central Tendency:
Mean
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Example:
A sample of five executives received the following bonus last year ($000):
, , , ,
$ 15,400
Every set of
interval- or ratio-level
data has a mean
All
the values are included in computing the mean
The mean is
unique
.
Central Tendency:
Mean
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
4. The
sum of the deviations of each value from the mean is
zero
.
Central Tendency:
Mean
Example:
Consider the set of values:
3, 8,
and
4
. The mean is
5
.
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Weighted Mean:
a set of numbers
X
1
,
X
2
, ...,
X
n
, with corresponding weights
w
1
,
w
2
, ...,
w
n
, is computed from the following formula:
Central
Tendency
:
Weighted
Mean
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Weighted Mean
:
Example:
During a one hour period on a hot Saturday afternoon, Julie served fifty lemon drinks. She sold
five drinks for $
,
fifteen for $
,
fifteen for $
, and
fifteen for $
. Compute the weighted mean of the price of the drinks.
Central
Tendency
:
Weighted
Mean
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Exercise
P62.
The
Bookstall
sold
books
via internet. Paperbacks are $
each
, and hardcover
books
are $. Of the 50
books
sold
on
last
Tuesday
, 40
were
paperback and the rest
were
hardcover.
What
was the
weighted
mean
price
of a
book
?
40 paperback
$
10 hardcover
$
a. $ b. $ c.$ d.$
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mode
Mode:
There is one situation in which the mode is the only measure of central tendency that can be used – when we have categorical, or non-numeric data. In this situation, we cannot calculate a mean or a median. The mode is the most typical value of the
categorical data
.
Example:
Suppose I have collected data on religious affiliation of citizens of the . The modal, or most Typical value, is Roman Catholic, since The
Roman Catholic
Church is the largest religious organization in the .
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mode
Mode:
The value of the observation that appears most frequently.
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mode
Mode:
The value of the observation that appears
most frequently
.
Example:
The exam scores for ten students are:
81
, 93, 84, 75, 68, 87, 81, 75, 81, 87.
Because the score of
81
occurs the most often, it is the mode.
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Median
Median:
the
midpoint
of the values after they have been ordered from the smallest to the largest.
Example:
The ages for a sample of five college students are:
21, 25, 19, 20, 22
Arranging the data in ascending order gives:
19, 20,
21
, 22, 25
.
Thus the median is
21
.
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Median
For an
even
set of values, the median will be the
arithmetic average of the two middle numbers
.
Example:
The heights of four basketball players, in inches, are:
76, 73, 80, 75
Arranging the data in ascending order gives:
73,
75, 76
, 80
. Thus the median is
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Median
72 68 65 70 75 79 73
Example:
Finding
the
median
65 68 70 72 73 75 79
65
68
70
72
73 75 79
79
65
68 70 72
73 75 79 79,000
Median
is
not
influenced
by
the extreme
value
.
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
P65.
Mean= ; Median=33; Mode=15
List
below
are the
total
automobile
sales
(in
millions
of dollars)
for
the last
7
years
.
What
was the
median
number
of automobiles
sold
?
What
is the mode?
41 15 39 54 31 15 33
Review
Chapter
3-A:
Central
Tendency
A.
Grouped
Data
a.
Mean
b. Mode
c.
Median
B.
Ungrouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
P69.
Central
Tendency
Mean
, Mode,
Median
Review
Chapter
3-A:
Central
Tendency
A.
Grouped
Data
a.
Mean
b. Mode
c.
Median
B.
Ungrouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mean
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mean
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mean
P87.
Determine
the
mean
of the
following
frequency
distribution.
a. b.
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Mode
Example:
Finding
the mode
for
grouped
data
Step 1:
Modal class with the highest frequency
Step 2:
Midpoint of the modal class is the mode
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Median
Example:
Finding
the
median
for
grouped
data
Step 1:
Cumulative
Frequency
Distribution
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Median
Step 2:
Determine
the
position
of the
median
and the
median
class
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
Central
Tendency
:
Median
Step 3:
Draw
two
lines
(
value
&
position
)
=
A
B
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
P87
SCCoast
, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users.
Describe the central tendency:
Mode
= 45 (years)
Median
= ? (years)
Exercise
a. b. e.
a. b. e.
a. b. e.
Review
Chapter
3-A:
Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a
.
Mean
b
. Mode
c
.
Median
P87
L
m
=(60+1)/2=
Median=
years
Step 1: Define the location of the median
Step 2: Calculate the median
M
Exercise
a. b. e.
What we have
learnt?
Review
Chapter
3-A: Central
Tendency
A.
Ungrouped
Data
a.
Mean
b. Mode
c.
Median
B.
Grouped
Data
a.
Mean
b. Mode
c.
Median
8. The Relative Positions of the
Mean
,
Median
, and Mode
Chapter 3: Describing Data
skewed
8. The Relative Positions of the
Mean
,
Median
, and Mode
Chapter 3: Describing Data
Zero skewness
mode=median=mean
7. The Relative Positions of the
Mean
,
Median
, and Mode
Chapter 3: Describing Data
positive skewness
Mode median mean
< <
8. The Relative Positions of the
Mean
,
Median
, and Mode
Chapter 3: Describing Data
negative skewness
Mode median mean
> >
8. The Relative Positions of the
Mean
,
Median
, and Mode
Chapter 3: Describing Data
