1. Descriptive Statistics

2. Coefficient of Variation
Summary Measures
Summary Measures
Central Tendency
Variation
Quartile
Mean
Mode
Coefficient of Variation
Median
Range
Variance
Standard Deviation
Geometric Mean
© 2002 Prentice-Hall, Inc.

3. Measures of Central Tendency
Average
Median
Mode
Geometric Mean
© 2002 Prentice-Hall, Inc.

4. Mean (Arithmetic Mean)
Mean (arithmetic mean) of data values
Sample mean
Population mean
Sample Size
Population Size
© 2002 Prentice-Hall, Inc.

5. Mean (Arithmetic Mean)
(continued)
The most common measure of central tendency
Affected by extreme values (outliers)
Mean = 5
Mean = 6
© 2002 Prentice-Hall, Inc.

6. Median Robust measure of central tendency
Not affected by extreme values
In an ordered array, the median is the “middle” number
If n or N is odd, the median is the middle number
If n or N is even, the median is the average of the two middle numbers
Median = 5
Median = 5
© 2002 Prentice-Hall, Inc.

7. Mode A measure of central tendency Value that occurs most often
Not affected by extreme values
Used for either numerical or categorical data
There may may be no mode
There may be several modes
No Mode
Mode = 9
© 2002 Prentice-Hall, Inc.

8. Geometric Mean
Useful in the measure of rate of change of a variable over time
Geometric mean rate of return
Measures the status of an investment over time
© 2002 Prentice-Hall, Inc.

9. Example
An investment of $100,000 declined to $50,000 at the end of year one and rebounded to $100,000 at end of year two:
© 2002 Prentice-Hall, Inc.

10. Quartiles Split Ordered Data into 4 Quarters Position of i-th Quartile
and Are Measures of Noncentral Location
= Median, A Measure of Central Tendency
25%
25%
25%
25%
Data in Ordered Array:
© 2002 Prentice-Hall, Inc.

11. Measures of Variation Variation Variance Standard Deviation
Coefficient of Variation
Range
Population
Variance
Population
Standard
Deviation
Sample
Variance
Sample
Standard
Deviation
Interquartile Range
© 2002 Prentice-Hall, Inc.

12. Range Measure of variation
Difference between the largest and the smallest observations:
Ignores the way in which data are distributed
Range = = 5
Range = = 5
© 2002 Prentice-Hall, Inc.

13. Interquartile Range Measure of variation Also known as midspread
Spread in the middle 50%
Difference between the first and third quartiles
Not affected by extreme values
Data in Ordered Array:
© 2002 Prentice-Hall, Inc.

14. Variance Important measure of variation Shows variation about the mean
Sample variance:
Population variance:
© 2002 Prentice-Hall, Inc.

15. Standard Deviation Most important measure of variation
Shows variation about the mean
Has the same units as the original data
Sample standard deviation:
Population standard deviation:
© 2002 Prentice-Hall, Inc.

16. Comparing Standard Deviations
Data A
Mean = 15.5
s = 3.338
Data B
Mean = 15.5
s = .9258
Data C
Mean = 15.5
s = 4.57
© 2002 Prentice-Hall, Inc.

17. Coefficient of Variation
Measures relative variation
Always in percentage (%)
Shows variation relative to mean
Is used to compare two or more sets of data measured in different units
© 2002 Prentice-Hall, Inc.

18. Comparing Coefficient of Variation
Stock A:
Average price last year = $50
Standard deviation = $5
Stock B:
Average price last year = $100
Coefficient of variation:
© 2002 Prentice-Hall, Inc.

19. Shape of a Distribution
Describes how data is distributed
Measures of shape
Symmetric or skewed
Left-Skewed
Symmetric
Right-Skewed
Mean < Median < Mode
Mean = Median =Mode
Mode < Median < Mean
© 2002 Prentice-Hall, Inc.

20. Exploratory Data Analysis
Box-and-whisker plot
Graphical display of data using 5-number summary
Median( ) X X
largest
smallest 4 6 8 10 12
© 2002 Prentice-Hall, Inc.

21. Distribution Shape and Box-and-Whisker Plot
Left-Skewed
Symmetric
Right-Skewed
© 2002 Prentice-Hall, Inc.

22. Coefficient of Correlation
Measures the strength of the linear relationship between two quantitative variables
© 2002 Prentice-Hall, Inc.

23. Features of Correlation Coefficient
Ranges between –1 and 1
The closer to –1, the stronger the negative linear relationship
The closer to 1, the stronger the positive linear relationship
The closer to 0, the weaker any positive linear relationship
© 2002 Prentice-Hall, Inc.

24. Scatter Plots of Data with Various Correlation CoefficientsY Y Y X X X
r = -1
r = -.6
r = 0 Y Y X X
r = .6
r = 1
© 2002 Prentice-Hall, Inc.

25. Task
Gunakan semua data yang telah anda miliki, untuk membuat descriptive statistics, selengkap mungkin.

26. Present Data

27. Organizing Numerical Data
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Frequency Distributions
Cumulative Distributions
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Ogive
3 028
4 1
Histograms
Stem and Leaf
Display
Tables
Polygons
© 2002 Prentice-Hall, Inc.

28. Organizing Numerical Data
(continued)
Data in raw form (as collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Data in ordered array from smallest to largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Stem-and-leaf display:
4 1
© 2002 Prentice-Hall, Inc.

29. Tabulating and Graphing Numerical Data
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Frequency Distributions
Cumulative Distributions
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
4 1
Ogive
Histograms
Stem and Leaf
Display
Tables
Polygons
© 2002 Prentice-Hall, Inc.

30. Tabulating Numerical Data: Frequency Distributions
Sort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Find range: = 46
Select number of classes: 5 (usually between 5 and 15)
Compute class interval (width): 10 (46/5 then round up)
Determine class boundaries (limits): 10, 20, 30, 40, 50, 60
Compute class midpoints: 15, 25, 35, 45, 55
Count observations & assign to classes
© 2002 Prentice-Hall, Inc.

31. Frequency Distributions, Relative Frequency Distributions and Percentage Distributions
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Relative
Frequency
Percentage
Class Frequency
10 but under
20 but under
30 but under
40 but under
50 but under
Total
© 2002 Prentice-Hall, Inc.

32. Graphing Numerical Data: The Histogram
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
No Gaps Between Bars
Class Boundaries
Class Midpoints
© 2002 Prentice-Hall, Inc.

33. Graphing Numerical Data: The Frequency Polygon
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class Midpoints
© 2002 Prentice-Hall, Inc.

34. Tabulating Numerical Data: Cumulative Frequency
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Cumulative Cumulative
Class Frequency % Frequency
10 but under
20 but under
30 but under
40 but under
50 but under
© 2002 Prentice-Hall, Inc.

35. Graphing Numerical Data: The Ogive (Cumulative % Polygon)
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class Boundaries (Not Midpoints)
© 2002 Prentice-Hall, Inc.

36. Graphing Bivariate Numerical Data (Scatter Plot)
© 2002 Prentice-Hall, Inc.

37. Tabulating and Graphing Categorical Data:Univariate Data
Graphing Data
Tabulating Data
The Summary Table
Pie Charts
Pareto Diagram
Bar Charts
© 2002 Prentice-Hall, Inc.

38. Summary Table (for an Investor’s Portfolio)
Investment Category Amount Percentage
(in thousands $)
Stocks
Bonds CD
Savings
Total
Variables are Categorical
© 2002 Prentice-Hall, Inc.

39. Graphing Categorical Data: Univariate Data
Graphing Data
Pie Charts
Pareto Diagram
Bar Charts
Tabulating Data
The Summary Table
© 2002 Prentice-Hall, Inc.

40. Bar Chart (for an Investor’s Portfolio)
© 2002 Prentice-Hall, Inc.

41. Pie Chart (for an Investor’s Portfolio)
Amount Invested in K$
Savings
15%
Stocks
42%
CD 14%
Percentages are rounded to the nearest percent.
Bonds 29%
© 2002 Prentice-Hall, Inc.

42. Pareto Diagram Axis for bar chart shows % invested in each category
Axis for line graph shows cumulative % invested
© 2002 Prentice-Hall, Inc.

43. Tabulating and Graphing Bivariate Categorical Data
Contingency tables: investment in thousands of dollars
Investment Investor A Investor B Investor C Total Category
Stocks
Bonds CD
Savings
Total
© 2002 Prentice-Hall, Inc.

44. Tabulating and Graphing Bivariate Categorical Data
Side by side charts
© 2002 Prentice-Hall, Inc.

45. Principles of Graphical Excellence
Presents data in a way that provides substance, statistics and design
Communicates complex ideas with clarity, precision and efficiency
Gives the largest number of ideas in the most efficient manner
Almost always involves several dimensions
Tells the truth about the data
© 2002 Prentice-Hall, Inc.

46. Errors in Presenting Data
Using “chart junk”
Failing to provide a relative basis in comparing data between groups
Compressing the vertical axis
Providing no zero point on the vertical axis
© 2002 Prentice-Hall, Inc.

47. “Chart Junk”  Bad Presentation Good Presentation $ 4 2 1960 1970 1980
Minimum Wage
Minimum Wage $
1960: $1.00 4
1970: $1.60 2
1980: $3.10
1990: $3.80
1960
1970
1980
1990
© 2002 Prentice-Hall, Inc.

48. A’s received by students. A’s received by students.
No Relative Basis 
Bad Presentation
Good Presentation
A’s received by students.
A’s received by students.
Freq. %
300 30
200 
 10  FR SO JR SR FR SO JR SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior
© 2002 Prentice-Hall, Inc.

49. Compressing Vertical Axis
Bad Presentation
Good Presentation
Quarterly Sales
Quarterly Sales $ $
200 50
100 25 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4
© 2002 Prentice-Hall, Inc.

50. No Zero Point on Vertical Axis
Bad Presentation
Good Presentation
Monthly Sales
Monthly Sales $ $ 45 45 42 42 39 39 36 36 J F M A M J J F M A M J
Graphing the first six months of sales.
© 2002 Prentice-Hall, Inc.

51. Task
Presentasikan semua data yang anda miliki, kedalam bentuk yang sesuai