Introductory of Business statistics International Business School Hanze University of Applied Sciences

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: Dispersion
• Range
• Variance (SD2)
• Standard Deviation (SD)
• Coefficient of variation (CV)
• Chapter 4: Displaying and exploring data
• Dotplot
• Stem-leaf
• Boxplot
• Skewness

3. Review
a b
Review
Chapter 3:
Discrete counting Continuous measuring
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and 1.Age 5. Salary
exploring data
–Dotplot
–Stem-leaf
2.Sales volume 6. Class size
–Boxplot
–Skewness 3. Temperature 7. Height
4. Weight 8. Shoe size (NL)

4. Review
Constructing Frequency Distribution: Quantitative Data
a. 4 b.5 c.6 d.70
25 = 32, 26 = 64, suggests 6 classes
Use interval of 100
a. 80 b.100 c.120 d.150
i> 571- 41 = 88.33
6
P46. N.30 Ch.2

5. Review
0 Cumulative
Class interval = 100
relative
relative
P46. N.30 Ch.2

6. Central Tendency : Mean, Mode, Median
Mean: Average
SCCoast, an Internet provider in the Southeast, developed the
following frequency distribution on the age of Internet users.
Describe the central tendency:
X = 2410 / 60 = 40.17 (years)
P87 N.60 Ch.3

7. Review
Central Tendency : Mean, Mode, Median
Mean: Average Mode: Most Frequency
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)
P87 N.60 Ch.3

8. Review
Central Tendency : Mean, Mode, Median
Mean: Average Mode: Most Frequency Median: Midpoint
SCCoast, an Internet provider in the Southeast, developed the
following frequency distribution on the age of Internet users.
Describe the central tendency:
a.40.25
b.41.25
c.30.50
d.37.50
Median = ? (years)
P87 N.60 Ch.3

9. Review
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
P87 N.60 Ch.3

10. Dispersion
Review
Range
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
Variance (SD2) and Standard Deviation (SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
Interquartile Range
exploring data
–Dotplot
–Stem-leaf
–Boxplot Coefficient of variation (CV)
–Skewness

11. Dispersion
Review
– tells us about the spread of the data.
Chapter 3:
– Help us to compare the spread in two or more
Dispersion distributions.
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

12. Dispersion: Range
Review Range:
Chapter 3: is the difference between the largest and
Dispersion
–Range the smallest value in a data set.
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Example:
Chapter 4:
Displaying and To find the range in 3,5,7,3,11
exploring data
–Dotplot
–Stem-leaf Range = 11-3 = 8
–Boxplot
–Skewness

13. Dispersion: Variance
Review
Population Variance:
• is the mean of the squared difference between each
Chapter 3:
Dispersion value and the mean.
–Range • overcomes the weakness of the range by using all the
–Variance (SD2)
–Standard Deviation values in the population.
(SD)
–Coefficient of
variation (CV) Σ(X - μ) 2
σ2 =
Chapter 4: N
Displaying and
exploring data
–Dotplot
–Stem-leaf
Sample Variance:
–Boxplot
Σ(X - X) 2
–Skewness
s2 =
n -1

14. EXAMPLE – Variance Variance
Dispersion: and Standard
Deviation
Population Variance: Σ(X - μ) 2
σ2 =
Review N
The number of traffic citations issued during the last five months in
Chapter 3:
Dispersion
Beaufort County, South Carolina, is 38, 26, 13, 41, and 22. What
–Range is the population variance?
–Variance (SD2)
–Standard Deviation Step 2: Find the difference between each observation and the mean
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and Step 1: Get the mean
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Step 3: Square the difference and sum up Step 4: Divided by N
27

15. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
Population Standard Deviation:
–Range
–Variance (SD2)
is the square root of the population variance.
–Standard Deviation
σ= σ2
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot Sample Standard Deviation:
–Stem-leaf
–Boxplot is the square root of the sample variance.
–Skewness
s = s2

16. Dispersion: Standard Deviation
Example:
Review The hourly wages earned by a sample of five students are:
€7, €5, €11, €8, €6.
Chapter 3:
Dispersion Find the variance and standard deviation.
–Range
Step 1: Get the mean ΣX 37
–Variance (SD2) X= = = 7.40
–Standard Deviation
(SD)
n 5
2
Σ(X - X )
2 2
–Coefficient of
Step 2: Sum up the (7 - 7.4) + ... + (6 - 7.4)
variation (CV)
squared differences s2 = =
n -1 5 -1
Chapter 4:
21.2
Displaying and
= = 5.30
exploring data
–Dotplot
Step 3: Divided by N-1 5 -1
–Stem-leaf
–Boxplot
–Skewness Step 4: Square root it s = €2.30
The variance is €5.30; the standard deviation is €2.30.

17. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
Compare
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of 20 40 50 60 80 20 49 50 51 80
variation (CV)
Chapter 4:
Displaying and
Step 1: Get the mean
exploring data
–Dotplot
–Stem-leaf Step 2: Sum up the
–Boxplot
squared differences
–Skewness
Step 3: Divided by N-1
Step 4: Square root it

18. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
Compare
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of 20 40 50 60 80 20 49 50 51 80
variation (CV)
Chapter 4:
Displaying and
exploring data •The sales of
–Dotplot
–Stem-leaf MANGO is more
–Boxplot
–Skewness closely clustered
around the mean
of 50 than the
sales of ZARA.

19. Dispersion: Standard Deviation
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
The standard deviation decreases because the new value 20 is very close to
the mean 20.36.

20. Dispersion: Standard Deviation
Step 1: Step 3: Use f * (Mid-Mean)2
Find the Midpoint
Step 2:
Calculate the Mean
P87 N.60 Ch.3

21. Dispersion: Standard Deviation
Step 4:
Calculate the Variance
Step 5:
Calculate the Standard Deviation
P87 N.60 Ch.3

22. Dispersion: Coefficient of Variation
Review
Coefficient of Variation:
Chapter 3: describes the magnitude sample values and the variation within
Dispersion them.
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
The following times were recorded by the quarter-mile and mile runners of a
Chapter 4: university track team (times are in minutes).
Displaying and
exploring data Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99
–Dotplot
–Stem-leaf Mile Times: 4.52 4.35 4.60 4.70 4.50
–Boxplot After viewing this sample of running times, one of the coaches commented that
–Skewness
the quarter milers turned in the more consistent times. Calculate the appropriate
measure to check this and comment on the coach’s statement.
We can compare the dispersion with the coefficient of variation because they
have different “magnitudes”.

23. Dispersion: Coefficient of Variation
Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99
Mile Times: 4.52 4.35 4.60 4.70 4.50

24. Dispersion: Coefficient of Variation
The following times were recorded by the quarter-mile and mile runners of a
Review university track team (times are in minutes).
Chapter 3:
Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99
Dispersion
Mile Times: 4.52 4.35 4.60 4.70 4.50
–Range
–Variance (SD2) After viewing this sample of running times, one of the coaches commented that
–Standard Deviation the quarter milers turned in the more consistent times. Calculate the appropriate
(SD) measure to check this and comment on the coach’s statement.
–Coefficient of
variation (CV) We can compare the dispersion with the coefficient of variation because they
have different “magnitudes”.
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
No, the mile-time team showed more consistent times.

25. Displaying and Exploring Data
Review Dot plots:
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

26. Displaying and Exploring Data
Review Stem-and-Leaf Displays:
Chapter 3: Each numerical value is divided into two parts. The leading
Dispersion
–Range
digit(s) becomes the stem and the trailing digit the leaf. The
–Variance (SD2) stems are located along the vertical axis, and the leaf values are
–Standard Deviation
(SD) stacked against each other along the horizontal axis.
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
Stem

27. Displaying and Exploring Data
Stem-and-Leaf Displays:
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

28. Displaying and Exploring Data
Review Quartiles, Deciles, and Percentiles
Chapter 3:
Alternative ways of describing spread of data include determining
Dispersion the location of values that divide a set of observations into equal
–Range parts.
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

29. Displaying and Exploring Data
Review
Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

30. Displaying and Exploring Data
Review
Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion Raw Percentile
–Range
Score Frequency Frequency Rank
–Variance (SD2)
–Standard Deviation
(SD) 95 1 25 100
–Coefficient of 93 1 24 96
variation (CV)
88 2 23 92
Chapter 4: 85 3 21 84
Displaying and
exploring data 79 1 18 72
–Dotplot 75 4 17 68
–Stem-leaf
–Boxplot 70 6 13 52
–Skewness 65 2 7 28
62 1 5 20
58 1 4 16
54 2 3 12
50 1 1 4
N = 25

31. Displaying and Exploring Data
Review
Quartiles, Deciles, and Percentiles
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV) Example:
Chapter 4:
Displaying and 101 43 75 61 91 104
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
The first quartile is ?

32. Displaying and Exploring Data
Review
Chapter 3: Step 1: Organize the data from lowest to largest value
Dispersion
–Range 101 43 75 61 91 104
–Variance (SD2)
–Standard Deviation
P1 P2 P3 P4 P5 P6
(SD)
–Coefficient of
variation (CV) Step 2: P1.75
Chapter 4:
Displaying and
exploring data
Step 3: Draw two lines
–Dotplot
–Stem-leaf
–Boxplot
–Skewness 43 61-43 = 18 61
P1 0.75 P2

33. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
Step 3: Draw two lines
(SD)
–Coefficient of
variation (CV) 43+13.5 = 56.5
Chapter 4:
Displaying and 43 61-43 = 18 61
exploring data
–Dotplot
–Stem-leaf
–Boxplot
P1 0.75 * 18 = 13.5 P2
–Skewness
The first quartile is 56.5.

34. Displaying and Exploring Data
Listed below, ordered from smallest to largest, are the number
of visits last week.
a. Determine the median number of calls.
a. 57median is 58.
The b.58 c.59 d.56
b. Determine the first and third quartiles.
Q1 = 51.25 Q3 = 66.00
a. 50.25 b.51.25 c.60.00 d.62.25 e.63.00 f. 66.00
P110. N.14 Ch.4

35. Displaying and Exploring Data
Listed below, ordered from smallest to largest, are the number of
visits last week.
c. Determine the first decile and the ninth decile.
D1 = 45.30 D9 = 76.40
d. Determine the 33rd percentile.
P33 = 53.53
P110. N.14 Ch.4

36. Displaying and Exploring Data
Review
Box Plots
A graphical display, based on quartiles to visualize a set of data.
Chapter 3:
Dispersion
–Range
minimum Q1 Median Q3 maximum
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

37. Displaying and Exploring Data
Review
Box Plots
A graphical display, based on quartiles to visualize a set of data.
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation minimum Q1 Median Q3 maximum
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

38. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and Zero skewness positive skewness negative skewness
exploring data
–Dotplot mode=median=mean Mode < Median < Mean Mode > Median > Mean
–Stem-leaf
–Boxplot
–Skewness

39. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness

40. Displaying and Exploring Data
Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness
minimum Q1 Median Q3 maximum

41. Review
Chapter 3:
Dispersion
–Range
–Variance (SD2)
–Standard Deviation
(SD)
–Coefficient of
variation (CV)
Chapter 4:
Displaying and
exploring data
–Dotplot
–Stem-leaf
–Boxplot
–Skewness •The graph is called a cumulative frequency distribution.
•The interquartile range is 45-35=10 years and the median is 40 years
a. 10 b.35 c.40 d.45 e.15 f.20
•50% of the employees are between 35 years and 45 years old.

42. What we have learnt?
1. Why Failed in
Statistics?
• Review
2. Chapter 1:
What is • Chapter 3: Dispersion
Statistics?
A.Why? What? • Range
B.Types of
statistics, • Variance (SD2)
variables
C.Levels of • Standard Deviation (SD)
measurement
• Coefficient of variation (CV)
3. Chapter 2:
Describing Data • Chapter 4: Displaying and exploring data
A.Frequency
tables
• Dotplot
B.Frequency • Stem-leaf
distributions
C.Graphic • Boxplot
presentation
• Skewness