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Transcript of Lesson07
IBS Statistics Year 1
Dr. Ning DING [email protected]
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Population:
Sample:
Play
Qualitative:Qualitative:
Quantitative: Quantitative: Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Discrete counting
Continuous measuring
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Interval: Interval:
Ratio: Ratio:
Ordered, Equal differences
Zero
Nominal: Nominal:
Ordinal: Ordinal:
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Frequency Table:
Relative Class Frequencies:
Frequency Distribution
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
25 75 125 175 225 275 325 375 42502468
10121416 Amount of € spent on books by 50
students
Amount in €
No.
of s
tude
ntsHistogram
Polygon
125 175 225 275 325 375 42502468
10121416 Amount of € spent on books by
50 students
Amount in €
No.
of s
tude
nts
Cumulative frequency distribution:
100 150 200 250 300 350 400 4500
102030405060
Amount of € spent on books by 50 students
Amount in €Cum
ulati
ve fr
eque
ncy
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Central Tendency
Mean
Median
Mode
Arithmatic Mean
Weighted Mean
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Example: During a one hour period on a hot Saturday afternoon, Julie served fifty lemon drinks. She sold five drinks for $0.50, fifteen for $0.75, fifteen for $0.90, and fifteen for $1.10. Compute the weighted mean of the price of the drinks.
$0.89=50
$44.50=
15+15+15+515($1.15)+15($0.90)+15($0.75)+5($0.50)
=Xw
Frequency counts
Weighted Mean
Central Tendency
Mean
Median
Mode
Arithmatic Mean
Weighted Mean
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Central Tendency
Mean
Median
Mode
Arithmatic Mean
Weighted Mean
Qualitative Data
Quantitative Data
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Central Tendency
Mean
Median
Mode
Arithmatic Mean
Weighted Mean
Qualitative Data
Quantitative Data
32
Recall in Chapter 2, we constructed a frequency distribution for the vehicle selling prices. The information is repeated below. Determine the arithmetic mean vehicle selling price.
The Arithmetic Mean of Grouped Data -Example
19.5
Draw two lines (value & position)
Value: 100 Median 150
Position: 201 300.5 388
Grouped Data
Ungrouped Data
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Coefficient of VariationThis is the ratio of the standard deviation to the mean:
The coefficient of variation describes the magnitude sample values and the variation within them.
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Measures of Dispersion
Range
Variance
Standard Deviation
Nμ)-Σ(X
=σ2
2Population
Sample
σPopulation
Sample
1-NXmean)-Σ(X
=SD2
2
SD
Schiphol 20 40 50 60 80
Utrecht 20 49 50 51 80
• The number of coffee sales in Utrecht Starbucks is more closely clustered around the mean of 50 than for the sales number in Schiphol
Starbucks.
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Box Plots
minimumminimum Q1Q1 MedianMedian Q3Q3 maximummaximum
Q1 Q3
Interquartile Range
Range
YX
Independent Variable
Dependent Variable
Ŷ = a + bX
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Least Square Equation:
Slope=5.75
Intercept=27.2857
r 2 = coefficient of determination
r = coefficient of correlation
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
r 2 = coefficient of determination
r = coefficient of correlation
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Remove trend, cyclical and irregular components from Y
Seasonal Index:
Remove the seasonal fluctuations in order to study the trend
Deseasonalizing Data:
Predicting Data:
• Using deseasonalized data to formulate Least Square Equation Ŷ =a + b t
• Times seasonal index
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
200520062007200820092010
Step 1: Re-organize the dataStep 1: Re-organize the data
Seasonal Index:
6.7+4.6+10.0+12.7=34 /4=8.504.6+10.0+12.7+6.5=33.8 /4=8.45
Step 2: Moving AverageStep 2: Moving AverageSeasonal Index:
Step 3: Centered Moving AverageStep 3: Centered Moving AverageSeasonal Index:
Step 4: Specific Seasonal IndexStep 4: Specific Seasonal IndexSeasonal Index:
10/8.475=1.18012.7/8.45=1.5036.5/8.425=0.772
Step 4: Specific Seasonal IndexStep 4: Specific Seasonal Index
Seasonal Index:
200520062007200820092010
+ + + =
Step 5: Typical Quarterly IndexStep 5: Typical Quarterly Index
*(0.9978) *(0.9978) *(0.9978) *(0.9978)
Seasonal Index:
200520062007200820092010
Step 6: InterpretStep 6: Interpret
Sales for the Fall are 51.9% above the typical quarter.
Sales for the Winter are 23.5% below the typical quarter.
Seasonal Index:
5. Deseasonalizing DataChapter 16: Time Series & Forecasting
76.5 57.5 114.1 151.9
/ 0.765 = 8.759
/ 0.575 = 8.004
/ 1.141 = 8.761/ 1.519 = 8.361
/ 0.765/ 0.575
/ 1.141/ 1.519/ 0.765/ 0.575
/ 1.141/ 1.519
= 8.498= 8.004
= 8.586= 8.953= 9.021= 8.700
= 9.112= 9.283
Deseasonalizing Data:
Ŷ = a + btŶ = a + bt
Ŷ = 8.1096 + 0.0899 tŶ = 8.1096 + 0.0899 t
Sale increased at a rate of 0.0899 ($ millions) per quarter.
Ŷ = 8.1096 + 0.0899 * 25= 10.3571 $ millions
10.3571*0.765 = 7.9232 $ millions
Chapter 16: Time Series & Forecasting
76.5 57.5 114.1 151.9
Predicting Data:
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Coding the time series?
Chapter 1: What is Statistics?
Chapter 2: Describing data-
Freaquency Table/Distribution
Chapter 3: Describing data-Numerical Measures
Chapter 4: Describing data-Displaying & Exploring data
Chapter 12: Correlational Analysis
Chapter 16: Time Series & Forecasting
Deseasonalization: Study the trend
How to prepare for STA1?Summary of the reasons
Absent for the lessons;
Didn’t do the home assignments;
Ignore the EXCEL lessons;
Cannot use the theories flexibly;
Keep misconceptions and misunderstanding till the exam;
Overestimate self and underestimate the subject.
How to prepare for STA1?
EXCEL Lesson Answer sheets
Mocked Exam
Books and Syllabus
PPT files
Blackboard Course Documents …