Chap 1 Statistik

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BEKA2453

STATISTICS & NUMERICAL

METHOD

Chapter 1

Introduction to StatisticsMiss Arfah Ahmad


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Learning OutcomeAt the end of the chapter you should be able to:

Study the basic introductory concept of

statistics including the branches of statistics,

the basic terms of statistics and types of

variables.

Use graphical and numerical methods to

describe a data set.


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What is Statistics The science of collecting, organizing,

summarizing and analyzing information in

order to draw conclusions.

Types of statistics:

1. Descriptive statistics

2. Inferential statistics


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What is Statistics DescriptiveStatistics

organizing and summarizing the informationcollected. Descriptive statistics describes the

information collected through numericalmeasurements, charts, graphs

Inferential Statistics

uses the methods that generalize resultsobtained from a sample to the population andmeasure their reliability.


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Basic terms Population consists of all items

Sample certain elements in the population(subset of population)

Random Sample

sample drawn in such away that each element of the population hasthe chance of being selected.

Element/number

a specific subject or

individual about which the information iscollected.


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Basic terms Variable characteristic of the individual within

the sample/population.

Observation/Measurement the value of a

variable for an element. Data Set collection of values of one or more

variables.

Ungrouped data set contains information ofeach member of a sample or population.

Grouped data set collection of data set whichare grouped in classes.


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Variables Qualitative Variables

- classification based on some attribute or

characteristics.

- ex: gender, marital status, type of cars

Quantitative Variables

- numerical measures

- ex: weight, height, number of cars owned,

student marks


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Variables Quantitative Variables

(a) Discrete variablescountable / finite

number of possible values

(b) Continuous variablesinfinite number

and uncountable. Obtain by measuring;include fractions and decimals


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Graphical Methods Frequency distributions

Bar graph

Pie chart Histogram

Polygon


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Numerical Measures

Relationship between mean, mode & median

Measures of Central

Tendency

Measures of Dispersion

Mean Range

Median Variance

Mode Standard deviation

Skewness


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Measures of CentralTendency - POPULATION Mean

the average

Median

- value that lies in the middle

- Calculation : based on grouped or ungroupeddata.

Mode

- the most frequent observation of the variable

that occurs in the data set. Skewness

- the measure of asymmetry of the data set.


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Measures of Dispersion -POPULATION Range

- difference between the largest data value andthe smallest data value.

Variance- the difference between each observation andthe mean; based upon the deviation about themean.

Standard Deviation- how closely the values of the data set areclustered around the mean

- the spread of the distribution


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Mean

Variance

Standard deviation

POPULATION1 2 1...

N

i

N i

X

X X X

N N

2

12 2

1

1

N

iN

ii

i

X

XN N

2

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iN

i

i

i

X

XN N


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SAMPLINGReasons to sample:

To contact the whole population would be timeconsuming

The cost of studying the all items in populationmay be prohibitive

The physical impossibility of checking all items inthe population

The destructive nature of some tests

The sample results are adequate


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Measures of CentralTendency - SAMPLE Mean

Median

Mode

Skewness


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Measures of Dispersion -SAMPLE Range

Variance

Standard Deviation


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SAMPLE Mean

Variance

Standard deviation

1 2 1...

n

i

N ixx x x

xn n

2

12 2

1

1

1

n

in

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2

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n

in

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Chap 1 Statistik

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