Statistic Course

Chapter 1

Statisticsby

Mohamed ELhusseiny

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IntroductionIntroduction

Statistics is the sciences of converting data to

information.

Statistics is a group of methods that are used to

collect, analyze, present, and interpret data and make

decisions

Types of statistics

Generally speaking there are to types of

statistics

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IntroductionIntroduction

Generally speaking there are to types of statistics

Descriptive statistics

The type of statistics that is used to organize, summarize and describe

the given data

Inferential statistics

The type of statistics that is uses a portion (A sample) of a large group

of elements ( A population) to get information about the population

instead of using the whole population that could be economically

expensive.

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IntroductionIntroduction

inferential statistics

consists of methods that use sample results to help make

decisions or predictions about a population.

Population versus samplePopulation versus sample

A population consists of all elements (individuals, items, or A population consists of all elements (individuals, items, or

objects) whose characteristics are being studiedobjects) whose characteristics are being studied

A sample of the population is a subset of this populationA sample of the population is a subset of this population

A population A sample

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Types of Variables and types of dataTypes of Variables and types of data

The variables used by statistics is usually classified based The variables used by statistics is usually classified based

on there types. There are two types of variableson there types. There are two types of variables

Variables

Discrete Continuous

Type of Data (Quantitative)

Type of Data

(Qualitative)

Numerical DataNominal Data Ordinal Data

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Types of data Types of data

Numerical (Interval) Data: data that are measured, such as,

time, age, weight, money, distance, amount of rain,…

Nominal data: data that are used to describe an event, such as

gender, blood type, marital status, number of care accidents per year,

….

Ordinal data: data that are used to describe an event but in a given

order, such as weather condition, course evaluation, Quality of a

magazine,…

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Graphical techniques for description of Graphical techniques for description of datadata

Type of Data

Numerical DataNominal Data Ordinal Data

Box plotsBar, Pie, and Line Charts

Histogram, Ogive, Stem and Leaf, and Box plots

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Graphical techniques for description of Graphical techniques for description of datadata

Blood Type

0

20

40

60

80

100

120

140

160

A B AB O

Blood TypeBlood Type FrequencyAA 5050

BB 120120

ABAB 8080

OO 150150

totaltotal 400400

A B AB O

0

20

40

60

80

100

120

140

160

Blood Type Frequency

50

120

80

150

050100150200

A

B

AB

O

Bar ChartsBar Charts

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Graphical techniques for description of Graphical techniques for description of datadata

B; 120; 30%

A; 50; 13%

O; 150; 37%

AB; 80; 20%

Blood TypeBlood Type FrequencyAA 5050

BB 120120

ABAB 8080

OO 150150

totaltotal 400400

Frequency

A%13

B%30

AB%20

O%37

Pie ChartsPie Charts

Frequency

A; 50; 13%

; ;B120%30

; ;AB80%20

; ;O150%37

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Graphical techniques for description of Graphical techniques for description of datadata

Bar ChartsBar Charts

20

30

10

15

25

0

5

10

15

20

25

30

35Field FrequencyBusiness 20

Economics 30

Arts 10

Political sciences 15

Others 25

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Business; 20

Economics; 30Arts; 10

Political sciences;

15

Others; 25

Graphical techniques for description of Graphical techniques for description of datadata

Field Frequency Relative frequency Angle sizeBusiness 20 0.2 360*0.2=72

conomics 30 0.3 360*0.3=108

Arts 10 0.1 360*0.1=36

Political sciences 15 0.15 360*0.15=54

Others 25 0.25 360*0.25=90

Pie ChartsPie Charts

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Graphical techniques for description of Graphical techniques for description of datadata

Business; 20

Economics; 30Arts; 10

Political sciences;

15

Others; 25

Field Frequency Relative frequency Angle sizeBusiness 20 0.2 360*0.2=72

conomics 30 0.3 360*0.3=108

Arts 10 0.1 360*0.1=36

Political sciences 15 0.15 360*0.15=54

Others 25 0.25 360*0.25=90

Pie ChartPie Chart

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Graphical techniques for description of Graphical techniques for description of datadata

HistogramHistogram

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HistogramHistogram

Question:How do I choose the number of classes and the width of the classes to be used in constructing a frequency distribution?

Answer: Although this choice is arbitrary and no hard and fast rules can be given, here are a few useful guidelines:

1. The classes must be nonoverlapping, so that each measurement falls into exactly one class. Therefore, choose the classes so that no measurement falls on a class boundary.The number of classes can be chosen by Struges’ formula

Number of classes = 1+3.3 log (nn)Where nn is the size of the data

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2. Choose the number of classes to be used as a number between 5 and 20, with smaller numbers of classes being chosen for smaller data sets. The approximate width of each class is given by the following:

Choose the actual class width to be a value close to the approximate width that is convenient to work with. Avoid awkward fractional values.

Graphical techniques for description of Graphical techniques for description of datadata

ClassesofNumber

valueMinimumvalueMaximumWidthclasseapproximat

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Example Example

The weights in pounds of a group of workers are as follows:

173 165 171 175 188183 177 160 151 169162 179 140 171 175168 158 186 182 162154 180 164 166 157 Construct a frequency distribution for these data.

HistogramHistogram

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Steps to construct the Histogram

1- choosing the No. of classes: Number of classes = 1+3.3 log (n)

= 1+3.3 log (25) = 5.6 = 5 or 6

2- Approximate Class width = (188 – 140 ) / 5 = 48/5 = approxi. 10

HistogramHistogram

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Steps to construct the Histogram

1- choosing the No. of classes: Number of classes = 1+3.3 log (n)

= 1+3.3 log (25) = 5.6 = 5 or 6

2- Approximate Class width = (188 – 140 ) / 5 = 48/5 = approxi. 10

HistogramHistogram

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Shapes of HistogramShapes of HistogramHistogramHistogram

1- Symmetry1- Symmetry

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Shapes of HistogramShapes of HistogramHistogramHistogram

1- Skewness1- Skewness

Positively Skewed Histogram

Negatively Skewed Histogram

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Shapes of HistogramShapes of HistogramHistogramHistogram

1- Number of Modal Classes1- Number of Modal Classes

Unimodal Histograms

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Shapes of HistogramShapes of HistogramHistogramHistogram

1- Number of Modal Classes1- Number of Modal Classes

Bimodal Histograms

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Thank youThank you