Introductory Statistics Hanze University of Applied Sciences International Business School (IBS)

1. Hanze University of
Applied Science
Groningen
Ning Ding, PhD
Lecturer of International Business
School (IBS)
n.ding@pl.hanze.nl

2. 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

3. Review
Review
A. Nominal B. Ordinal C. Interval D. Ratio
Chapter 3-A:
Central Tendency
A. Ungrouped Data What is the level of measurement for these items related to
a. Mean the newspaper business?
b. Mode
c. Median
a. The number of papers sold each Sunday during 2006.
B. Grouped Data
a. Mean
b. The departments, such as editorial, advertising , sports, etc.
b. Mode
c. Median
c. A summary of the number of papers sold by county.
d. The number of years with the paper for each employee.
P14. N.2 Ch.1

4. Review
Review A. Sample B. Population
Chapter 3-A:
Central Tendency For the follow questions, would you collect information using
a sample or a population?
A. Ungrouped Data
a. Mean
b. Mode a. Statistics 201 is a course taught at a university. Professor A has
c. Median taught nearly 1,500 students in the course over the past 5
years. You would like to know the average grade for the course
B. Grouped Data
a. Mean
b. Mode
c. Median
b. 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. N.8 Ch.1

5. Review
Review
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median

6. Review
Review
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median

7. Review
Review
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean A
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median
A (21, 30) Around _______of the vehicles were seld below $21,000.
a. 30% b. 43% c. 35 d. 43

8. Review
A set of data contains 53 observations. The lowest value is 43 and the largest is
Review
129. The data are to be organized into a frequency distribution.
a. How many classes would you suggest?
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean
b. Mode 25 4 32, 265= 64, suggests 6 classes
a. = b. c. 6 d. 7
c. Median
B. Grouped Data b. What would you suggest as class interval & the lower limit of
a. Mean the first class?
b. Mode
c. Median a. 10 130 - 4318
b. 15 c. d. 20
i> ≈ 15
6
Use interval of 15
And start first class at 40
P34. N.10 Ch.2

9. Central Tendency
Parameter:
Review
a numerical characteristic of a
Chapter 3-A: population.
Central Tendency
Example: The fraction of U. S. voters who
A. Ungrouped Data support Sen. McCain for President is a
a. Mean
b. Mode
parameter.
c. Median
B. Grouped Data Statistic:
a. Mean A statistic is a numerical characteristic of a sample.
b. Mode
c. Median
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.

10. 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

11. Central Tendency: Mean
Sum of all the values in the population
Review
Population mean =
Number of values in the population
Chapter 3-A:
Central Tendency
μ=
∑X
A. Ungrouped Data
Example: N
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median

12. Central Tendency: Mean
Example:
Review
A sample of five executives received the following bonus last year
Chapter 3-A: ($000):
Central Tendency 14.0, 15.0, 17.0, 16.0, 15.0
ΣX 14.0+ ... +15.0 77
A. Ungrouped Data
a. Mean
b. Mode X= = = = 15.4
c. Median
n 5 5
B. Grouped Data
a. Mean
b. Mode
1. Every set of interval- or ratio-level data has a mean
c. Median
2. All the values are included in computing the mean
3. The mean is unique.

13. Central Tendency: Mean
Example:
Review
Consider the set of values: 3, 8, and 4. The mean is 5.
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean Σ(X - X) = (3 - 5) + (8 - 5) + (4 - 5) = 0
b. Mode
c. Median
4. The sum of the deviations of each value from
the mean is zero.

14. Central Tendency: Mean
Review
Weighted Mean:
Chapter 3-A: a set of numbers X1, X2, ..., Xn, with corresponding weights
Central Tendency
w1, w2, ...,wn, is computed from the following formula:
A. Ungrouped Data
a. Mean
b. Mode
c. Median
(w 1 X1 + w 2 X 2 + ... + w n X n )
B. Grouped Data Xw =
a. Mean
b. Mode
(w 1 + w 2 + ...w n )
c. Median

15. Central Tendency: Mean
Weighted Mean:
Review Example:
Chapter 3-A: During a one hour period on a hot Saturday
Central Tendency afternoon, Julie served fifty lemon drinks.
She sold five drinks for $0.50, fifteen for
A. Ungrouped Data
a. Mean $0.75, fifteen for $0.90, and fifteen for $1.10.
b. Mode Compute the weighted mean of the price of
c. Median the drinks.
B. Grouped Data
a. Mean
b. Mode
c. Median
5($0.50)+15($0.75)+15($0.90)+15($1.10)
Xw =
5 +15 +15 +15
$44.50
= = $0.89
50

16. Exercise
(w 1 X 1 + w 2 X 2 + ... + w n X n )
Xw =
Review (w 1 + w 2 + ...w n )
Chapter 3-A: The Bookstall sold books via internet. Paperbacks are $1.00
Central Tendency
each, and hardcover books are $3.50. Of the 50 books sold on
A. Ungrouped Data last Tuesday, 40 were paperback and the rest were hardcover.
a. Mean What was the weighted mean price of a book?
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median
(40 * $1.00+10 * $3.50)
Xw = $1.50
50
a. $1.50 b. $1.54 c.$1.60 d.$1.64
P62. N.14 Ch.3

17. Central Tendency: Mode
Mode:
Review
There is one situation in which the mode is the only
Chapter 3-A: measure of central tendency that can be used – when
Central Tendency we have categorical, or non-numeric data. In this
situation, we cannot calculate a mean or a median. The
A. Ungrouped Data
a. Mean mode is the most typical value of the categorical data.
b. Mode
c. Median
B. Grouped Data
Example:
a. Mean Suppose I have collected data on religious affiliation of citizens of
b. Mode the U.S. The modal, or most Typical value, is Roman
c. Median Catholic, since The Roman Catholic Church is the largest religious
organization in the U.S.

18. Central Tendency: Mode
Mode:
Review
The value of the observation that appears most frequently.
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median

19. Central Tendency: Mode
Mode:
Review
The value of the observation that appears most
Chapter 3-A: frequently.
Central Tendency
Example:
A. Ungrouped Data
a. Mean
The exam scores for ten students are:
b. Mode
c. Median 81, 93, 84, 75, 68, 87, 81, 75, 81, 87.
B. Grouped Data
a. Mean
b. Mode
c. Median Because the score of 81 occurs the most often, it is the mode.

20. Central Tendency: Median
Median:
Review
the midpoint of the values after they have been ordered
Chapter 3-A:
from the smallest to the largest.
Central Tendency
A. Ungrouped Data
a. Mean
Example:
b. Mode The ages for a sample of five college students are:
c. Median
21, 25, 19, 20, 22
B. Grouped Data
a. Mean
b. Mode Arranging the data in ascending order gives:
c. Median 19, 20, 21, 22, 25.
Thus the median is 21.

21. Central Tendency: Median
Review
For an even set of values, the median will be the
Chapter 3-A:
Central Tendency arithmetic average of the two middle numbers.
A. Ungrouped Data
a. Mean
b. Mode Example:
c. Median The heights of four basketball players, in inches, are:
B. Grouped Data
a. Mean 76, 73, 80, 75
b. Mode
c. Median
Arranging the data in ascending order gives:
73, 75, 76, 80. Thus the median is 75.5

22. Central Tendency: Median
Example:
72 68 65 70 75 79 73
Review
Finding the median
Chapter 3-A:
Central Tendency
65 68 70 72 73 75 79
A. Ungrouped Data
a. Mean
b. Mode
c. Median 65 68 70 72 73 75 79 79
B. Grouped Data
a. Mean 72.5
b. Mode
c. Median
65 68 70 72 73 75 79 79,000
72.5
Median is not influenced by the extreme value.

23. Exercise
Review
List below are the total automobile sales (in millions
Chapter 3-A: of dollars) for the last 7 years. What was the median
Central Tendency
number of automobiles sold? What is the mode?
A. Ungrouped Data 41 15 39 54 31 15 33
a. Mean
b. Mode
c. Median
B. Grouped Data
Mean= 32.57; Median=33; Mode=15
a. Mean
b. Mode
c. Median
P65. N.22 Ch.3

24. Exercise
Review
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean Mean Mode Median
b. Mode
City
c. Median
- - -
B. Grouped Data
Wind
a. Mean - Southwest -
b. Mode
direction
c. Median
Temperature 91 o F 92 o F 92 o F
Pavement - Wet & Dry Trace

25. ample
he Arithmetic Mean of Grouped Data -
xample Central Tendency: Mean
call in Chapter 2, we
constructed a frequency
Recall in Chapter 2, we
Review
distribution forfrequency
the vehicle
constructed a
selling prices. The
Chapter 3-A:
distribution for the vehicle
Central Tendency
information is repeated
selling prices. The
information is repeated
below. Determine the
A. Ungrouped Data
a. Mean
below. Determine the
arithmetic mean vehicle
b. Mode
arithmetic mean vehicle
c. Median
selling price.
selling price.
B. Grouped Data
a. Mean
b. Mode
c. Median
33

26. he Arithmetic Mean of Grouped Data
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

27. Central Tendency: Mean
Review
Chapter 3-A:
Central Tendency Determine the mean of the following frequency distribution.
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median
a. 15.00 b. 12.54 c.11.54 d.12.67
X=380/30=12.67 P87. N.58 Ch.3

28. Central Tendency: Mode
, we
Review
Example: Finding the mode for grouped data
equency Step 1:
Chapter 3-A:
Step 2:
he vehicleModal class with the highest frequency Midpoint of the modal class
Central Tendency
is the mode
heA. Ungrouped Data
a. Mean
peated
b. Mode
c. Median
ne the
B. Grouped Data
vehicle
a. Mean
b. Mode 19.5
c. Median

29. Central Tendency: Mode
Example: Finding the mode for grouped data
Review
Chapter 3-A:
Step 1:
Central Tendency
Modal class with the highest frequency
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median

30. Central Tendency: Mode
Step 2:
Review Midpoint of the modal class is the mode
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median

31. Central Tendency: Median
Step 3:
Review
Chapter 3-A:
Draw two lines (value & position)
Central Tendency
A. Ungrouped Data Value: 100 A Median 150
a. Mean
b. Mode Position: 201 300.5 B 388
c. Median
B. Grouped Data
a. Mean Median – 100 300.5 – 201
b. Mode =
c. Median
150 - 100 388 - 201
300.5 – 201
Median = * 50 + 100 = 126.60 (dollars)
388 - 201

32. Exercise
SCCoast, an Internet provider in the Southeast, developed the following frequency
distribution on the age of Internet users. Describe the central tendency:
Review
Chapter 3-A:
Central Tendency
A. Ungrouped Data
a. Mean
b. Mode
c. Median
B. Grouped Data
a. Mean
b. Mode
c. Median
Mode = 45 (years)
X=
a. 20.00
a. 30.50
2410 / 60c.45.00 d.45.50 e. 50.00
b. 40.00
b. 38.00
= 40.17 (years)
c.38.25 d.40.25 e. 41.25 f.50.50
f.42.25
a. 40.17 b. 200.83 c.482.00 d.120.50 e. 48.20
Median = ? (years)
P87 N.60 Ch.3

33. Exercise
a. 30.00 b. 38.00 c.38.25 d.40.25 e. 41.25 f.42.25
Step 1: Define the location of the median Step 2: Calculate the median
M
Lm=(60+1)/2=30.5 Value:40 50
Location: 28 48
30.5
30.5-28 M-40
=
48-28 50-40
Median= 41.25 years
P87 N.60 Ch.3

34. What we have learnt?
• Review
Review
Chapter 3-A:
Central Tendency
• Chapter 3-A: Central Tendency
A. Ungrouped
A. Ungrouped Data
Data
a. Mean
a. Mean
b. Mode
c. Median
b. Mode
B. Grouped Data
c. Median
a. Mean
b. Mode
B. Grouped Data
c. Median
a. Mean
b. Mode
c. Median