ISTANBUL STOCK EXCHANGE (BIST) FELL 6 POINTS IN AVERAGE TODAY

THE UNITED STATES DOLLAR (USD) APPRECIATED BY 4 PERCENT LAST WEEK AGAINST TURKISH LIRA (TRL). AT THE 95% CONFIDENCE LEVEL, IT IS

ESTIMATED THAT THE EXCHANGE RATE WILL BE BETWEEN _____ AND ____.

THE LATEST SURVEY INDICATES THAT THE PRESIDENT`S APPROVAL RATING

NOW STANDS AT 60 PERCENT

THE PRICE OF KOC HOLDING STOCK WILL BE HIGHER IN SIX MONTH THAN IT IS NOW

THE PRICE OF KOC HOLDING STOCK IS LIKELY TO BE HIGHER IN SIX MONTH THAN IT IS NOW

THE STAGES FOR STATISTICAL THINKING ARE:

1- DEFINE THE PROBLEM

2- DETERMINE WHAT DATA IS NEEDED

3- SELECT A SAMPLE

4- COLLECT DATA

5- SUMMARIZE AND ANALYZE DATA

6- MAKE INFERENCES AND DECISIONS BASED ON INFORMATION

The Journey to Making Decisions

Begin Here:Identify the

ProblemDATADATA

INFORMATION

KNOWLEDGE

DECISIONMAKING

Descriptive Statistics, Probability, Computers

Experience, Theory, Literature

Inferential Statistics, Computers

DATA: Specific observations of measured numbers.

INFORMATION: Processed and summarized data yielding facts and ideas.

KNOWLEDGE:Selected and organized information that providesunderstanding, recommendations, andthe basis for decisions.

Descriptive Statistics include graphical and numerical procedures that summarize and process data and are used

to transform data into information

Descriptive Statistics include graphical and numerical procedures that summarize and process data and are used

to transform data into information

Inferential Statistics provide the bases for predictions, forecasts, and estimates that are to transform information to knowledge

Descriptive Statistics include graphical and numerical procedures that summarize and process data and are used

to transform data into information

Descriptive Statistics include graphical and numerical procedures that summarize and process data and are used

to transform data into information

POPULATION: A complete set of individuals, objects or

measurements having common observable characteristics.

Examples of Populations

- Names of all registered voters in TURKEY

- Incomes of all families living in ANKARA

- Annual return of all stocks traded on the ISTANBUL STOCK EXCHANGE

- Grade Point Averages of all the students in your University - BILKENT

SAMPLE: A subset or part of a population

Examples of Samples

- Names of 50.000 registered voters in TURKEY

- Incomes of 10.000 families living in ANKARA

- Annual return of 150 stocks traded on the ISTANBUL STOCK EXCHANGE

- Grade Point Averages of 500 students from different departments in your University - BILKENT

Example:

Imagine that a public opinion polling firm has been contracted to conduct a study concerning the percentage of the state`s registered voters who approve of nuclear power as an energy source. As part of the polling process, 750 individuals are randomly selected from the voter registration list and carefully interviewed.

Elements?

Random Sample ?

Variable of Interest?

Data?

Statistic?

Population?

Below AverageBelow Average Above AverageAbove Average Above AverageAbove Average AverageAverage Above Average Above Average AverageAverage Above AverageAbove Average

Average Average Above AverageAbove Average Below AverageBelow Average PoorPoor Excellent Excellent Above AverageAbove Average AverageAverage

Above AverageAbove Average Above AverageAbove Average Below AverageBelow Average PoorPoor Above Average Above Average AverageAverage

Frequency DistributionFrequency Distribution Example: Marada InnExample: Marada Inn

Sample of Parts Cost($) for 50 Tune-Sample of Parts Cost($) for 50 Tune-upsups

Frequency DistributionFrequency Distribution

Example: Hudson Auto RepairExample: Hudson Auto Repair

Dot PlotDot Plot

5050 6060 7070 8080 9090 100100 1101105050 6060 7070 8080 9090 100100 110110

Cost ($)Cost ($)

Tune-up Parts CostTune-up Parts Cost

Example: Hudson Auto RepairExample: Hudson Auto Repair

Stem-and-Leaf DisplayStem-and-Leaf Display

55

66

77

88

99

1010

2 72 7

2 2 2 2 5 6 7 8 8 8 9 9 92 2 2 2 5 6 7 8 8 8 9 9 9

1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 91 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9

0 0 2 3 5 8 90 0 2 3 5 8 9

1 3 7 7 7 8 91 3 7 7 7 8 9

1 4 5 5 91 4 5 5 9

a stema stema leafa leaf

Example: Hudson Auto RepairExample: Hudson Auto Repair

Note: Data is in ascending order.Note: Data is in ascending order.

525 530 530 535 535 535 535 535 540 540540 540 540 545 545 545 545 545 550 550550 550 550 550 550 560 560 560 565 565565 570 570 572 575 575 575 580 580 580580 585 590 590 590 600 600 600 600 610610 615 625 625 625 635 649 650 670 670675 675 680 690 700 700 700 700 715 715

Measures of LocationMeasures of Location

MeanMean

MedianMedian

ModeMode PercentilesPercentiles QuartilesQuartiles

Weighted MeanWeighted Mean

Sample Mean Sample Mean xx

Number ofNumber ofobservationsobservationsin the samplein the sample

Sum of the valuesSum of the valuesof the of the nn observations observations

ixx

n ix

xn

Population Mean Population Mean

Number ofNumber ofobservations inobservations inthe populationthe population

Sum of the valuesSum of the valuesof the of the NN observations observations

ix

N

ix

N

Weighted MeanWeighted Mean

Denominator:Denominator:sum of thesum of the

weightsweights

Numerator:Numerator:sum of the weightedsum of the weighted

data valuesdata values

i i

i

wxx

w

i i

i

wxx

w

where:where:

xxii = value of observation = value of observation ii

wwi i = weight for observation = weight for observation ii

Weighted MeanWeighted Mean

Example: Construction WagesExample: Construction Wages

Ron Butler, a home builder, is looking over Ron Butler, a home builder, is looking over the expenses he incurred for a house he just the expenses he incurred for a house he just built. For the purpose of pricing future projects, built. For the purpose of pricing future projects, he would like to know the average wage ($/hour) he would like to know the average wage ($/hour) he paid the workers he employed. Listed below he paid the workers he employed. Listed below are the categories of worker he employed, along are the categories of worker he employed, along with their respective wage and total hours with their respective wage and total hours worked.worked.

Worker Wage ($/hr) Total Hours

Carpenter 21.60 520Electrician 28.72 230

Laborer 11.80 410Painter 19.75 270Plumber 24.16 160

Weighted MeanWeighted Mean

Example: Construction WagesExample: Construction Wages

31873.720.0464 $20.05

1590i i

i

wx

w

31873.7

20.0464 $20.051590

i i

i

wx

w

Worker x i wi wi x i

Carpenter 21.60 520 11232.0 Electrician 28.72 230 6605.6

Laborer 11.80 410 4838.0 Painter 19.75 270 5332.5 Plumber 24.16 160 3865.6

1590 31873.7

FYI, equally-weighted (simple) mean = FYI, equally-weighted (simple) mean = $21.21$21.21

8080thth Percentile Percentile

ii = ( = (pp/100)/100)nn = (80/100)70 = 56 = (80/100)70 = 56

Averaging the 56Averaging the 56thth and 57 and 57thth data values: data values:

80th Percentile = (635 + 649)/2 = 64280th Percentile = (635 + 649)/2 = 642

Note: Data is in ascending order.Note: Data is in ascending order.

Example: Apartment RentsExample: Apartment Rents

525 530 530 535 535 535 535 535 540 540540 540 540 545 545 545 545 545 550 550550 550 550 550 550 560 560 560 565 565565 570 570 572 575 575 575 580 580 580580 585 590 590 590 600 600 600 600 610610 615 625 625 625 635 649 650 670 670675 675 680 690 700 700 700 700 715 715

525 530 530 535 535 535 535 535 540 540540 540 540 545 545 545 545 545 550 550550 550 550 550 550 560 560 560 565 565565 570 570 572 575 575 575 580 580 580580 585 590 590 590 600 600 600 600 610610 615 625 625 625 635 649 650 670 670675 675 680 690 700 700 700 700 715 715

8080thth Percentile Percentile

““At least 80% of theAt least 80% of the items take on aitems take on a

value of 642 or less.”value of 642 or less.”

““At least 20% of theAt least 20% of theitems take on aitems take on a

value of 642 or more.”value of 642 or more.”

56/70 = .8 or 80%56/70 = .8 or 80% 14/70 = .2 or 20%14/70 = .2 or 20%

Example: Apartment RentsExample: Apartment Rents

QuartilesQuartiles

Quartiles are specific percentiles.Quartiles are specific percentiles. First Quartile = 25th PercentileFirst Quartile = 25th Percentile

Second Quartile = 50th Percentile = MedianSecond Quartile = 50th Percentile = Median Third Quartile = 75th PercentileThird Quartile = 75th Percentile

A wholesaler sold 575, 410 and 520 microwave ovens at prices (in USD) 75, 125 and 100 respectively. What is the mean price of the ovens sold?

Example:

The following data represent the duration (in days) of Space Shuttle voyages for the years 1992-1994. (18 values)

8,9,9,14,8,8,10,7,6,9,7,8,10,14,11,8,14,11

Q: Find The Mode

MONTHLY STARTING SALARY (In TRL)

Graduate Monthly Starting Salary

1 2,850

2 2,950

3 3,050

4 2,880

5 2,755

6 2,710

7 2,890

8 3,130

9 2,940

10 3,325

11 2,920

12 2,880

TOTAL: 35,280