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Introduction to Applied Statistics

- CHAPTER 1
- BCT2053

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

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.

1.1 OVERVIEW

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.

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

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

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

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)

An overview of descriptive statistics and

statistical inference

Descriptive Statistics

Yes

Statistical Inference

No

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.

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.

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.

1.2 STATISTICAL PROBLEM SOLVING METHODOLOGY

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

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)

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.

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)

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.

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

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.

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.

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.

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.

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?

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.

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.

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)

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

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

- 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?

Level of Measurements of Data

Examples

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)

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.

Statistical Problem Solving Methodology

No

Yes

Yes

No

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

1.3 REVIEW OF DESCRIPTIVE STATISTICS

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

- 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

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

- 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

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.

- 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

- 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

Types of Distribution

Symmetric

Positively skewed or right-skewed

Negatively skewed or left-skewed

- 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

- 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

- 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

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.

Chebychev Theorem

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

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.

Thank You

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

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