Introduction to Applied Statistics

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Introduction to Applied Statistics

• CHAPTER 1
• BCT2053

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CONTENT

• 1.1 Overview
• 1.2 Statistical Problem-Solving Methodology
• 1.3 Review of Descriptive Statistics
• 1.3.1 Measures of Central Tendency
• 1.3.2 Measures of Variation

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OBJECTIVE

• By the end of this chapter, you should be able to
• Define the meaning of statistics, population,
  sample, parameter, statistic, descriptive
  statistics and inferential statistics.
• Understand and explain why a knowledge of
  statistics is needed
• Outline the 6 basic steps in the statistical
  problem solving methodology.
• Identifies various method to obtain samples.
• Discuss the role of computers and data analysis
  software in statistical work.
• Summarize data using measures of central
  tendency, such as the mean, median, mode, and
  midrange.
• Describe data using measures of variation, such
  as the range, variance, and standard deviation.

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1.1 OVERVIEW
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What is Statistics?
Most people become familiar with probability and
statistics through radio, television, newspapers,
and magazines. For example, the following
statements were found in newspapers

• Ten of thousands parents in Malaysia have chosen
  StemLife as their trusted stem cell bank.
• The average annual salary for a professional
  football player for the year 2001 was 1,100,500.
• The average cost of a wedding is nearly
  RM10,000.
• In USA, the median salary for men with a
  bachelors degree is 49,982, while the median
  salary for women with a bachelors degree is
  35,408.
• Globally, an estimated 500,000 children under
  the age of 15 live with Type 1 diabetes.
• Women who eat fish once a week are 29 less
  likely to develop heart disease.

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Statistics

• is the sciences of conducting studies to collect,
  organize, summarize, analyze, present, interpret
  and draw conclusions from data.

Any values (observations or measurements) that
have been collected
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The basic idea behind all statistical methods of
data analysis is to make inferences about a
population by studying small sample chosen from
it
Population The complete collection of
measurements outcomes, object or individual under
study
Parameter A number that describes a population
characteristics
Tangible Always finite after a population is
sampled, the population size decrease by 1 The
total number of members is fixed could be listed
Conceptual Population that consists of all the
value that might possibly have been observed
has an unlimited number of members
Sample A subset of a population, containing the
objects or outcomes that are actually observed
Statistic A number that describes a sample
characteristics
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Descriptive Inferential Statistics

• Inferential statistics
• consists of generalizing from samples to
  populations, performing estimations hypothesis
  testing, determining relationships among
  variables, and making predictions.
• Used to describe, infer, estimate, approximate
  the characteristics of the target population
• Used when we want to draw a conclusion for the
  data obtain from the sample

• Descriptive statistics
• consists of the collection, organization,
  classification, summarization, and presentation
  of data obtain from the sample.
• Used to describe the characteristics of the
  sample
• Used to determine whether the sample represent
  the target population by comparing sample
  statistic and population parameter

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Example 1

• Ten of thousands parents in Malaysia have chosen
  StemLife as their trusted stem cell bank.
  (Descriptive)
• The death rate from lung cancer was 10 times for
  smokers compared to nonsmokers. (Inferential)
• The average cost of a wedding is nearly
  RM10,000. (Descriptive)
• In USA, the median salary for men with a
  bachelors degree is 49,982, while the median
  salary for women with a bachelors degree is
  35,408. (Descriptive)
• Globally, an estimated 500,000 children under
  the age of 15 live with Type 1 diabetes.
  (Inferential)
• A researcher claim that a new drug will reduce
  the number of heart attacks in men over 70 years
  of age. (Inferential)

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An overview of descriptive statistics and
statistical inference
Descriptive Statistics
Yes
Statistical Inference
No
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Need for Statistics

• It is a fact that, you need a knowledge of
  statistics to help you
• Describe and understand numerical relationship
  between variables
• There are a lot of data in this world so we need
  to identify the right variables.
• Make better decision
• Statistical methods allow people to make better
  decisions in the face of uncertainty.

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Describing relationship between variables

• A management consultant wants to compare a
  clients investment return for this year with
  related figures from last year. He summarizes
  masses of revenue and cost data from both periods
  and based on his findings, presents his
  recommendations to his client.
• A college admission director needs to find an
  effective way of selecting student applicants. He
  design a statistical study to see if theres a
  significance relationship between SPM result and
  the gpa achieved by freshmen at his school. If
  there is a strong relationship, high SPM result
  will become an important criteria for acceptance.

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Aiding in Decision Making

• Suppose that the manager of Big-Wig Executive
  Hair Stylist, Alvin Tang, has advertised that
  90 of the firms customers are satisfied with
  the companys services. If Pamela, a consumer
  activist, feels that this is an exaggerated
  statement that might require legal action, she
  can use statistical inference techniques to
  decide whether or not to sue Alvin.
• Students and professional people can also use the
  knowledge gained from studying statistics to
  become better consumers and citizens. For
  example, they can make intelligent decisions
  about what products to purchase based on consumer
  studies about government spending based on
  utilization studies, and so on.

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1.2 STATISTICAL PROBLEM SOLVING METHODOLOGY
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STATISTICAL PROBLEM SOLVING METHODOLOGY

• 6 Basic Steps
• Identifying the problem or opportunity
• Deciding on the method of data collection
• Collecting the data
• Classifying and summarizing the data
• Presenting and analyzing the data
• Making the decision

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STEP 1Identifying the problem or opportunity

• Must clearly understand correctly define the
  objective/goal of the study
• If not, time effort are waste
• Is the goal to study some population?
• Is it to impose some treatment on the group
  then test the response?
• Can the study goal be achieved through simple
  counts or measurements of the group?
• Must an experiment be performed on the group?
• If sample are needed, how large?, how should they
  be taken? the larger the better (more than 30)

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Characteristics of sample size

• The larger the sample, the smaller the magnitude
  of sampling errors.
• Survey studies needed large sample because the
  returns of the survey is voluntary based.
• Easy to divide into subgroups.
• In mail response the percentage of response may
  be as low as 20-30, thus the bigger number of
  samples is required.
• Subject availability and cost factors are
  legitimate considerations in determining
  appropriate sample size.

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STEP 2Deciding on the Method of Data Collection

• Data must be gathered that are accurate, as
  complete as possible relevant to the problem
• Data can be obtained in 3 ways
• Data that are made available by others (internal,
  external, primary or secondary data)
• Data resulting from an experiment (experimental
  study)
• Data collected in an observational study
  (observation, survey, questionnaire, interview)

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STEP 3Collecting the data

• Nonprobability data
• Is one in which the judgment of the experimenter,
  the method in which the data are collected or
  other factors could affect the results of the
  sample
• 3 basic methods Judgment samples, Voluntary
  samples and Convenience samples
• Probability data
• Is one in which the chance of selection of each
  item in the population is known before the sample
  is picked
• 4 basic methods random, systematic, stratified,
  and cluster.

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Nonprobability data samples

• Judgment samples
• Base on opinion of one or more expert person
• Ex A political campaign manager intuitively
  picks certain voting districts as reliable places
  to measure the public opinion of his candidate
• Voluntary samples
• Question are posed to the public by publishing
  them over radio or tv (phone or sms)
• Convenience samples
• Take an easy sample (most conveniently
  available)
• Ex A surveyor will stand in one location ask
  passerby their questions

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Probability data samples

• Random samples
• Selected using chance method or random methods
• Example
• A lecturer wants to study the physical fitness
  levels of students at her university. There are
  5,000 students enrolled at the university, and
  she wants to draw a sample of size 100 to take a
  physical fitness test. She obtains a list of all
  5,000 students, numbered it from 1 to 5,000 and
  then randomly invites 100 students corresponding
  to those numbers to participate in the study.

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Probability data samples

• Systematic samples
• Numbering each subject of the populations and
  data is selected every kth number.
• Example
• A lecturer wants to study the physical fitness
  levels of students at her university. There are
  5,000 students enrolled at the university, and
  she wants to draw a sample of size 100 to take a
  physical fitness test. She obtains a list of all
  5,000 students, numbered it from 1 to 5,000 and
  randomly picks one of the first 50 voters
  (5000/100 50) on the list. If the pick number
  is 30, then the 30th student in the list should
  be invited first. Then she should invite the
  selected every 50th name on the list after this
  first random starts (the 80th student, the 130th
  student, etc) to produce 100 samples of students
  to participate in the study.

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Probability data samples

• Stratified samples
• Dividing the population into groups according to
  some characteristics that is important to the
  study, then sampling from each group
• Example
• A lecturer wants to study the physical fitness
  levels of students at her university. There are
  5,000 students enrolled at the university, and
  she wants to draw a sample of size 100 to take a
  physical fitness test. Assume that, because of
  different lifestyles, the level of physical
  fitness is different between male and female
  students. To account for this variation in
  lifestyle, the population of student can easily
  be stratified into male and female students. Then
  she can either use random method or systematic
  methods to select the participants. As example
  she can use random sample to chose 50 male
  students and use systematic method to chose
  another 50 female students or otherwise.

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Probability data samples

• Cluster samples
• Dividing the population into sections/clusters,
  then randomly select some of those cluster and
  then choose all members from those selected
  cluster
• Using a cluster sampling can reduce cost and
  time.
• Example
• A lecturer wants to study the physical fitness
  levels of students at her university. There are
  5,000 students enrolled at the university, and
  she wants to draw a sample to take a physical
  fitness test. Assume that, because of different
  lifestyles, the level of physical fitness is
  different between freshmen, sophomores, juniors
  and seniors students. To account for this
  variation in lifestyle, the population of student
  can easily be clustered into freshmen,
  sophomores, juniors and seniors students. Then
  she can choose any one cluster such as freshmen
  and take all the freshmen students as the
  participant.

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Identified the type of sampled obtain Example
1 A physical education professor wants to study
the physical fitness levels of students at her
university. There are 20,000 students enrolled at
the university, and she wants to draw a sample of
size 100 to take a physical fitness test. She
obtains a list of all 20,000 students, numbered
it from 1 to 20,000 and then invites the 100
students corresponding to those numbers to
participate in the study.
Example 2 A quality engineer wants to inspect
rolls of wallpaper in order to obtain information
on the rate at which flows in the printing are
occurring. She decides to draw a sample of 50
rolls of wallpaper from a days production. Each
hour for 5 hours, she takes the 10 most recently
produced rolls and counts the number of flaws on
each. Is this a simple random sample?
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Example 3 Suppose we have a list of 1000
registered voters in a community and we want to
pick a probability sample of 50. We can use a
random number table to pick one of the first 20
voters (1000/50 20) on our list. If the table
gave us the number of 16, the 16th voter on the
list would be the first to be selected. We would
then pick every 20th name after this random start
(the 36th voter, the 56th voter, etc) to produce
a sample. Example 4 Consumer surveys of large
cities often employ cluster sampling. The usual
procedure is to divide a map of the city into
small blocks each blocks containing a cluster are
surveyed. A number of clusters are selected for
the sample, and all the households in a cluster
are surveyed. Using a cluster sampling can reduce
cost and time. Less energy and money are expended
if an interviewer stays within a specific area
rather than traveling across stretches of the
cities.
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Example 5 Suppose our population is a university
student body. We want to estimate the average
annual expenditures of a college student for non
school items. Assume we know that, because of
different lifestyles, juniors and seniors spend
more than freshmen and sophomores, but there are
fewer students in the upper classes than in the
lower classes because of some dropout factor. To
account for this variation in lifestyle and group
size, the population of student can easily be
stratified into freshmen, sophomores, junior and
seniors. A sample can be stratum and each result
weighted to provide an overall estimate of
average non school expenditures. Example 6 A
research wanted to survey students in 100
homerooms in secondary school in a large school
district. They could first randomly select 10
schools from all the secondary schools in the
district. Then from a list of homerooms in the 10
schools they could randomly select 100.
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STEP 4Classifying and Summarizing the data

• Organize or group the facts/sample raw data for
  study and investigation
• Classifying- identifying items with like
  characteristics arranging them into groups or
  classes.
• Ex Production data (product make, location,
  production process ext..)
• Data can be classified as Qualitative
  (categorical/Attributes) data and Quantitative
  (Numerical) data.
• Summarization
• Graphical Descriptive statistics ( tables,
  charts, measure of central tendency, measure of
  variation, measure of position)

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Data Classification

• Data are the values that variables can assume
• Variables is a characteristic or attribute that
  can assume different values.
• Variables whose values are determined by chance
  are called random variables

Variables can be classified
By how they are categorized, counted or measured
- Level of measurements of data
As Quantitative and Qualitative
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Types of Data
Qualitative (categorical/Attributes) 1 Data that
refers only to name classification (done using
numbers) 2 Can be placed into distinct
categories according to some characteristic or
attribute.
Nominal Data (cant be rank) Gender, race,
citizenship. etc
Use code numbers (1, 2,)
Ordinal Data (can be rank) Feeling (dislike
like), color (dark bright) , etc
Discrete Variables Assume values that can be
counted and finite Ex no of something
Quantitative (Numerical) 1 Data that represent
counts or measurements (can be count or
measure) 2 Are numerical in nature and can be
ordered or ranked.
Continuous variables 1. Can assume all values
between any two specific values it obtained by
measuring 2. Have boundaries and must be rounded
because of the limits of measuring device Ex
weight, age, salary, height, temperature, etc
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• Example
• The Lemon Marketing Corporation has asked you
  for information about the car you drive. For each
  question, identify each of the types of data
  requested as either attribute data or numeric
  data. When numeric data is requested, identify
  the variable as discrete or continuous.
• What is the weight of your car?
• In what city was your car made?
• How many people can be seated in your car?
• Whats the distance traveled from your home to
  your school?
• Whats the color of your car?
• How many cars are in your household?
• Whats the length of your car?
• Whats the normal operating temperature (in
  degree Fahrenheit) of your cars engine?
• What gas mileage (miles per gallon) do you get in
  city driving?
• Who made your car?
• How many cylinders are there in your cars
  engine?
• How many miles have you put on your cars current
  set of tyres?

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Level of Measurements of Data
Examples
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STEP 5Presenting and Analyzing the data

• Summarized analyzed information given by the
  graphical descriptive statistics
• Identify the relationship of the information
• Making any relevant statistical inferences
  (hypothesis testing, confidence interval, ANOVA,
  control charts, etc)

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STEP 6Making the decision

• The researchers can make a list of all the
  options and decisions which can achieve the
  objective and goal of the research, weighs the
  options and choose the best options which
  represents the best solution to the problem.
• The correctness of this choice depends on the
  analytical skill and the quality of the
  information.

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Statistical Problem Solving Methodology
No
Yes
Yes
No
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Role of the Computer in Statistics

• Two software tools commonly used for data
• analysis
• Spreadsheets
• Microsoft Excel Lotus 1-2-3
• Statistical Packages
• MINITAB, SAS, SPSS and SPlus

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1.3 REVIEW OF DESCRIPTIVE STATISTICS
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Summary Statistics (Data Description)

• Statistical methods can be used to summarize
  data.
• Measures of average are also called measures of
  central tendency and include the mean, median,
  mode, and midrange.
• Measures that determine the spread of data values
  are called measures of variation or measures of
  dispersion and include the range, variance, and
  standard deviation.
• Measures of position tell where a specific data
  value falls within the data set or its relative
  position in comparison with other data values.
  The most common measures of position are
  percentiles, deciles, and quartiles.
• The measures of central tendency, variation, and
  position are part of what is called traditional
  statistics. This type of data is typically used
  to confirm conjectures about the data

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• 1.3.1 Measures of Central Tendency

Mean the sum of the values divided by the total
number of values.
Population Mean
Sample Mean
Example 9 2 1 4 3 3 7 5 8
6
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Properties of Mean

• The mean is compute by using all the values of
  the data.
• The mean varies less than the median or mode when
  samples are taken from the same population and
  all three measures are computed for these
  samples.
• The mean is used in computing other statistics,
  such as variance.
• The mean for the data set is unique, and not
  necessarily one of the data values.
• The mean cannot be computed for an open-ended
  frequency distribution.
• The mean is affected by extremely high or low
  values and may not be the appropriate average to
  use in these situations

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• 1.3.1 Measures of Central Tendency

Median the middle number of n ordered data
(smallest to largest)
If n is odd
If n is even
Example 9 2 1 4 3
3 7 5 8 6
Example 9 2 1 3 3
7 5 8 6
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Properties of Median

• The median is used when one must find the center
  or middle value of a data set.
• The median is used when one must determine
  whether the data values fall into the upper half
  or lower half of the distribution.
• The median is used to find the average of an
  open-ended distribution.
• The median is affected less than the mean by
  extremely high or extremely low values.

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• 1.3.1 Measures of Central Tendency

Mode the most commonly occurring value in a data
series

• The mode is used when the most typical case is
  desired.
• The mode is the easiest average to compute.
• The mode can be used when the data are nominal,
  such as religious preference, gender, or
  political affiliation.
• The mode is not always unique. A data set can
  have more than one mode, or the mode may not
  exist for a data set.

Example 9 2 1 4 3 3 7 5 8 6
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• 1.3.1 Measures of Central Tendency

Midrange is a rough estimate of the middle
also a very rough estimate of the average and can
be affected by one extremely high or low value.
Example 9 2 1 4 3 3 7 5 8 6
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Types of Distribution
Symmetric
Positively skewed or right-skewed
Negatively skewed or left-skewed
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• 1.3.2 Measures of Variation / Dispersion

• Used when the central of tendency doesn't mean
  anything or not needed (ex mean are same for two
  types of data)
• One that measure the variability that exists in a
  data set
• To form a judgment about how well the average
  value illustrate/ depict the data
• To learn the extent of the scatter so that steps
  may be taken to control the existing variation

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• 1.3.2 Measures of Variation / Dispersion

Range is the different between the highest
value and the lowest value in a data set. The
symbol R is used for the range.
R highest value - lowest value
Example 9 2 1 4 3 3 7 5 8 6
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• 1.3.2 Measures of Variation / Dispersion

Variance is the average of the squares of the
distance each value is from the mean.
Population Variance
Sample Variance
Population standard deviation , ?
Sample standard deviation, s
Example 9 2 1 4 3 3
7 5 8 6
Standard Deviation is the square root of the
variance
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Properties of Variance
Standard Deviation

• Variances and standard deviations can be used to
  determine the spread of the data. If the variance
  or standard deviation is large, the data are more
  dispersed. The information is useful in comparing
  two or more data sets to determine which is more
  variable.
• The measures of variance and standard deviation
  are used to determine the consistency of a
  variable.
• The variance and standard deviation are used to
  determine the number of data values that fall
  within a specified interval in a distribution.
• The variance and standard deviation are used
  quite often in inferential statistics.
• The standard deviation is used to estimate amount
  of spread in the population from which the sample
  was drawn.

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Chebychev Theorem
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TIPS Calculate mean and variance by
using Scientific Calculator

• Casio fx-570MS
• Insert data
• MODE SD data M
• Shift 1
• Shift 2
• Clear data
• Shift CLR 1

• Casio fx-570W
• Insert data
• MODE SD data M
• Shift 1
• Shift 2
• Shift 3
• Shift 4
• Clear data
• Shift AC/ON

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Conclusion

• The applications of statistics are many and
  varied. People encounter them in everyday life,
  such as in reading newspapers or magazines,
  listening to the radio, or watching television.
• By combining all of the descriptive statistics
  techniques discussed in this chapter together,
  the student is now able to collect, organize,
  summarize and present data.

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Thank You

• See You in CHAPTER 2
• SAMPLING DISTRIBUTION AND CONFIDENCE INTERVAL