University of Sulaimani
Civil Eng. Dept
Statistics. :2nd stage
University of Sulaimani
College of Engineering
Civil Engineering Department
Theory: 2 hrs
Tutorial: -Practical: -Units: 2
Term: One course
Statistics
Mid term exaam: each 20 marks
Quiz and homework, etc. : 20 marks
Prepared by : Ass. Prof. Dr. Hirsh M. Majid (‫ ه رش محمد مجيد‬.‫)د‬
Office: 3rd floor- Civil Engineering
Mail: hirsh.majid@univsul.edu.iq
Site: https://sites.google.com/a/univsul.edu.iq/hirsh-muhammad/
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Syllabus
Chapter 1 : Introduction
Chapter 2: Organizing data
Chapter 3: Descriptive measures
Chapter 4: Probability
Chapter 5: Discrete random variables
Chapter 6: Continuous random variables and their probability distributions
Chapter 7: Sampling distributions
Chapter 8: Estimation and sample size determination
Chapter 9: Tests of Hypothesis
Chapter 10: Chi-square procedures and Normal distribution
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References
• Schaum’s outlines: Beginning statistics, Larry J. Stephens
• Statistics, 4th ed. by David Freedman and Robert Pisani
• The Elements of Statistical Learning: Data Mining, Inference and Prediction, 2nd ed. by
Trevor Hastie and Robert Tibshirani
• Schaum’s outlines, Statistics, fourth edition, Murray R. Speigel, Ph.D. Larry J. Stephens,
Ph.D.
• Schaum’s outlines, Probability and Statistics, fourth edition, Murray R. Spiegel, PhD,
John Schiller, R. Alu Srinivasan
• Etc …..
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Statistics
Chapter one: Introduction
Statistics is the discipline that concerns the collection, organization, analysis,
interpretation and presentation of data.
OR
Statistics are the sets of mathematical equations that we used to analyze the things.
OR
Statistics is the science of learning from data.
- Statistics allows you to understand a subject much more deeply
- It keeps us informed about, what is happening in the world around us.
- It is used in a lot of application in a wide variety of disciplines; Engineering, Science,
Economy, Medicine, social life, …..
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The field of statistics is divided into two major divisions:
1. Descriptive statistics, and
2. Inferential statistics
Descriptive statistics: the use of graphs, charts, and tables and the calculation of various statistical
measures to organize and summarize information is called descriptive statistics.
There are a number of items that belong in this portion of statistics, such as:
The average, or measure of the center of a data set, consisting of the mean, median, mode, or
midrange
The spread of a data set, which can be measured with the range or standard deviation
Overall descriptions of data such as the five number summary
Measurements such as skewness and kurtosis
The exploration of relationships and correlation between paired data
The presentation of statistical results in graphical form
Inferential statistics:
Inferential statistics start with a sample and then generalizes to a population. This information
about a population is not stated as a number. Instead, scientists express these parameters as a
range of potential numbers, along with a degree of confidence.
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Variable, Observation, and Data set:
A characteristic of interest concerning the individual elements of a population or a sample is called
a variable. A variable is often represented by a letter such as x, y , or z. The value of a variable for
one particular element from the sample or population is called an observation. A data set consists
of the observations of a variable for the elements of a sample.
Six hundred registered voters are polled and each one is asked if they approve or disapprove of
the president’s economic policies. The variable is the registered voter’s opinion of the
president’s economic policies. The data set consists of 600 observations.
Variable: registered voter’s opinion
Observation: each person among the 600 voters
Data set: 600 observations
A survey of 2500 households headed by a single parent is conducted and one characteristic of
interest is the yearly household income.
Variable: household income
Observation: each household among 2500 household
Data set: 2500 household
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Quantitative variable: Discrete and continuous variable
A quantitative variable is determined when the description of the characteristic of interest
results in a numerical value.
A discrete variable : is a quantitative variable whose values are countable, usually result
from counting.
A continuous variable: is a quantitative variable that can assume any numerical value over
an interval or over several intervals, usually results from making a measurement of some
type.
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Qualitative variable: A qualitative variable is determined when the description of the
characteristic of interest results in a non-numerical value. A qualitative variable may be
classified into two or more categories.
Qualitative variable
Possible categories for the variable
Marital status
Single, married, divorced, separated
Gender
Male, female
Crime classification
Misdemeanor, felony
Pain level
None, low, moderate, severe
Personality type
Type A, Type B
The possible categorized for qualitative variables are often coded for the purpose of
performing computerized statistical analysis. Marital status might be coded as 1,2,3, or 4,
where 1 represents single, 2 represents married, 3 represents divorced, and 4 represents
separated.
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Nominal, Ordinal, Interval, and Ratio levels of measurement
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Nominal, Ordinal, Interval, and Ratio levels of measurement
There are four levels of measurement or scales of measurements into which data can be
classified. The nominal scale applies to data that are used for category identification. The
nominal level of measurement is characterized by data that consist of names, labels, or
categories only. Nominal scale data can not be arranged in an ordering scheme. The
arithmetic operations of addition, subtraction, multiplication, and division are not
performed for nominal data.
Qualitative variable: 1-Blood type. 2-Color of road signs in the Sulaimani city. 3-Religion
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Nominal, Ordinal, Interval, and Ratio levels of measurement
The ordinal scale applies to data that can be arranged in some order, but differences
between data values either cannot be determined or are meaningless. The ordinal level of
measurement is characterized by data that applies to categories that can be ranked.
Ordinal scale data can be arranged in an ordering scheme.
Qualitative variable:
Product rating : Poor, good, excellent
Socioeconomic class: Lower, middle and upper
Pain level: None, low, moderate, severe
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Nominal, Ordinal, Interval, and Ratio levels of measurement
The interval scale applies to data that can be arranged in some order and for which
differences in data values are meaningful. The interval level of measurement results from
counting or measuring. Interval scale data can be arranged in an ordering scheme and
differences can be calculated and interpreted.
For example: Temperatures represent interval level dada. The high temperature on
February equaled 25F and the high temperature on March equaled 50F. It was warmer on
March than it was on February. That is, temperatures can be arranged in order. It was 25F
warmer on March than on February. That is, differences may be calculated and
interpreted.
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Nominal, Ordinal, Interval, and Ratio levels of measurement
The ratio scale applies to data that can be ranked and for which all arithmetic operations
including division can be performed. Division by zero is, of course, excluded. The ratio
level of measurement results from counting or measuring. Ratio scale data can be
arranged in an ordering scheme and differences and ratios can be calculated and
interpreted.
For example: The grams of fat consumed per day for adults is ratio scale data. Mashxal
consumes 10 grams of fat per day and Zanyar consumes 20 grams per day. Zanyar
consumes twice as much fat as Mashxal per day, since 20/10=2.
- Good examples of ratio variables include height, weight, and duration.
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Summation notation
Example: Suppose the number of 112 emergency calls received on four days were
411,375, 400, and 478.
If we let x represent the number of calls received per day, then the values of the variable
for the four days are represented as follows:
X1 = 411, X2 = 375, X3 = 400, and X4 = 478
The sum of calls for the four days is X1+X2+X3+X4 which equals 411+375+400+478 = 1664
The symbol
, read as ‘the summation of x’ is used to represent X1+X2+X3+X4
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Example: The following five values were observed for the variable x: x1 = 4, x2=5, x3=0,
x4=6, and x5=10. The following computations illustrate the usage of the summation
notation.
=
=
=
=
=
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Example: The following values were observed for the variables x and y:
x1 = 1, x2 = 2, x3 = 0, x4=4. y1 = 2, y2 = 1, y3 = 4 y4 = 5.
The following computations show how the summation notation is used for two variables.
=
=
=
∑
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