1 Introduction (1)
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McGraw-Hill/ Irwin © The McGraw-Hill Companies, Inc., 2003 All Rights Reserved. 1-1 Chapter One What is What is Statistics? Statistics? GOALS When you have completed this chapter, you will be able to: ONE Understand why we study statistics. TWO Explain what is meant by descriptive statistics and inferential statistics. THREE Distinguish between a qualitative variable and a quantitative variable. FOUR Distinguish between a discrete variable and a continuous variable. FIVE Distinguish among the nominal, ordinal, interval, and ratio levels of measurement. SIX Understand how data are collected.
Transcript of 1 Introduction (1)
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Chapter OneWhat is What is Statistics?Statistics?GOALS
When you have completed this chapter, you will be able to:ONE Understand why we study statistics. TWO Explain what is meant by descriptive statistics and inferential statistics.THREEDistinguish between a qualitative variable and a quantitative variable.FOUR Distinguish between a discrete variable and a continuous variable.FIVEDistinguish among the nominal, ordinal, interval, and ratio levels of measurement. SIX Understand how data are collected.
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What is Meant by Statistics?
Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.
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Who Uses Statistics?
Statistical techniques are used extensively by managers in marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, etc...
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Types of StatisticsDescriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.EXAMPLE 1: A poll found that 49% of the people in a survey knew the name of the first President of the United States. The statistic 49 describes the number out of every 100 persons who knew the answer.
EXAMPLE 2: According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2002. The statistic 9 describes the number of problems out of every 100 machines.
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Types of Statistics Inferential Statistics: is concerned with making conclusions or inferences from samples about the populations from which they have been drawn.
Example: The researcher did an analysis to find out if it is true workers in Kuala Lumpur have to spend an average of at least RM400.00 a month on petrol..
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Types of Statistics(examples of inferential statistics)
O EXAMPLE 1: TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers.
EXAMPLE 2: The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company.
EXAMPLE 3: The quality control department tested a few microchips to make a decision with respect to all the microchips waiting to be released for sale.
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Application : Intranet?
Intranet is very important in any organisation that is trying to upgrade their communication system and provide a paperless working environment. Result of a survey done in one organisation is summarized in the following chart.
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Quick questions:
a. Who was surveyed?b. Are there more people who are satisfied than
are not satisfied (ignore adequate)?c. Do you know how many respondents there
are?
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Population
A population is a collection of all possible individuals, objects, or measurements of interest.
Example: All new students enrolled in the 2010/11 session at the RAZAK School of Engineering and Advanced Technology, UTM is the population.
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Sample
A sample is a portion, or part, of the population of interest
Example: First year students who are in the SHR Program are chosen.
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Variable
A variable is a particular characteristic of the object being studied. This characteristic can take on different values as we measure/gather it from one object to another.
Example: The new students have to provide information about their height, weight, previous school and parent’s income. These are the variables.
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Random
Randomness means unpredictability. One of the requirements in a sampling process is to conform to randomness. Hence the variable being measured is called a random variable.
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Data
Data are basically numbers derived from measuring or observing outcomes of a random variable. Since no two things are exactly alike, data can differ from item to item.
Example: For the random variable height we get data values such as 152 cm, 163.2 cm, 148.9 cm, …, etc.
Data can also be non-numeric. Example: Data on their previous schools could be
SMK Jaya Gading, SMK Bukit Kota, MRSM Bentong, …, etc.
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Types of Variables
For a Qualitative or Categorical variable the characteristic being studied is nonnumeric.
EXAMPLES: Gender, religious affiliation, type of automobile owned, state of birth, eye color are examples.
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Types of Variables
In a Quantitative variable information is reported numerically.
EXAMPLES: balance in your checking account, minutes remaining in class, or number of children in a family.
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Types of VariablesQuantitative variables can be classified as either discrete or continuous.
Discrete variables: Produces data that are whole numbers. It is usually derived from a counting process for example the number of students in a class are 30, 25, 65,…..
EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the local Home Depot (1,2,3,…,etc).
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Types of Variables
A continuous variable can assume any value within a specified range including fractions, decimals, and irrational numbers. .
Examples are: The pressure in a tire, the weight of a durian, or the height of students in a class.
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Summary of Types of Variables
Q u alita t ive o r a ttrib u te(typ e o f c a r ow n ed )
d is c re te(n u m b er o f c h ild ren )
con tin u ou s(t im e taken fo r an exam )
Q u an tita t ive or n u m eric a l
D A TA
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Quick questions
Qualitative or quantitative?a. Number of books read in a month: 5, 4, 7, 2.b. Time taken to finish a 100 metre run: 12.5
sec, 15.8 sec, 45.0 sec.c. Types of handphone: Nokia, Samsung. d. Academic year: 1st year, 2nd year, 3rd year.e. Subjects taken: Geometry, English, History.
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Levels of Measurement There are four levels of data measurement
scale.
Nominal scales classify data into various distinct categories.
EXAMPLES: eye color, gender, religious affiliation. Numbers can be assigned to these data as a representation. (for example male = 1, female = 2).
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Levels of MeasurementOrdinal level: involves data arranged in some order, but the differences between data values cannot be determined or are meaningless.
EXAMPLE: During a taste test of 4 soft drinks, Coke was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.
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Levels of Measurement
Interval scale involves numerical data but it does not have a true zero point.
Example: Temperature, whereby zero degrees Fahrenheit does not mean there is no temperature. Zero is an arbitrary value. Comparison between values is also relative, for example if it is 40oC outside and it is 20oC inside this room we cannot say it is twice as hot outside as it is inside this room.
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Levels of MeasurementRatio level is the interval level with a true zero starting point. Differences and ratios are meaningful for this level of measurement.
EXAMPLES: Covers most numerical measures such as salary, height, weight, etc. A person who has RM100 has twice as much as someone who only has RM50. And a person who has zero Ringgit in his pocket truly has no money!
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Quick questions
Now which of these are nominal,ordinal, discrete or continuous?
a. Number of books read in a month: 5, 4, 7, 2.b. Time taken to finish a 100 metre run: 12.5
sec, 15.8 sec, 45.0 sec.c. Types of handphone: Nokia, Samsung.d. Academic year: 1st year, 2nd year, 3rd year.e. Subjects taken: Geometry, English, History.
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Parameter
A parameter is a value used to represent a certain population characteristic. Parameters are assigned Greek letters, for example, mean is and standard deviation is .
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Statistic
A statistic is a numerical value summarizing some aspect of the sampled data. Most sample statistics are found using formulas. They are assigned Roman letters, for example, is mean and s is standard deviation.
x
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Data Collection
If data is collected from every unit in a population, then that is called a census.
Normally performed by government agencies only as the population is usually very large and the data collection process requires a lot of time and energy to conduct plus a high cost.
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Experimental Study The investigator applies a treatment on the object
and observes the effect on the variable they want to measure.
Examples:• scientific experiments done on rats such as
turning them diabetic and then seeing the effect of a new medication in lowering the blood glucose level of these rats.
• two different teaching methods are conducted and student’s performance from the two methods is compared.
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Observational Study Data is collected through observation without
applying any treatment on the object. This can be done through surveys or by just observing the behaviour of the object.
Example:• An investigator might just observe the behaviour
of consumers in a hypermarket to find out how they choose what they buy.
• A student leader might hand out questionnaires to the final year students to ask their opinion about the effectiveness of the Student Development Centre.
