Statistic Course Chapter 1 Statistics by Mohamed ELhusseiny
Jan 20, 2016
Statistic Course
Chapter 1
Statisticsby
Mohamed ELhusseiny
Monday 16-June-2003
2
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