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

http://mips.stanford.edu/courses/stats_data_analsys/lesson_1/234_0_a.html

Qualitative:Qualitative:

Quantitative: Quantitative: Chapter 1: What is Statistics?














Discrete counting

Continuous measuring








Interval: Interval:

Ratio: Ratio:

Ordered, Equal differences

Zero

Nominal: Nominal:

Ordinal: Ordinal:








Frequency Table:

Relative Class Frequencies:

Frequency Distribution








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








Central Tendency

Mean

Median

Mode

Arithmatic Mean

Weighted Mean








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








Central Tendency

Mean

Median

Mode

Arithmatic Mean

Weighted Mean

Qualitative Data

Quantitative Data








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








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.








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.








Box Plots

minimumminimum Q1Q1 MedianMedian Q3Q3 maximummaximum

Q1 Q3

Interquartile Range

Range

YX

Independent Variable

Dependent Variable

Ŷ = a + bX








Least Square Equation:

Slope=5.75

Intercept=27.2857

r 2 = coefficient of determination

r = coefficient of correlation















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








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


76.5 57.5 114.1 151.9

Predicting Data:








Coding the time series?








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 …

Lesson07

Technology

Transcript of Lesson07