Materi Statistik Bab 1 : Data dan Statistik
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Transcript of Materi Statistik Bab 1 : Data dan Statistik
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Slides Prepared byJOHN S. LOUCKS
St. Edward’s University
© 2002 South-Western /Thomson LearningTM
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Chapter 1 Data and Statistics
Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference
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Applications in Business and Economics
AccountingPublic accounting firms use statistical sampling procedures when conducting audits for their clients.
FinanceFinancial advisors use a variety of statistical information, including price-earnings ratios and dividend yields, to guide their investment recommendations.
MarketingElectronic point-of-sale scanners at retail checkout counters are being used to collect data for a variety of marketing research applications.
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ProductionA variety of statistical quality control charts are used to monitor the output of a production process.
EconomicsEconomists use statistical information in making forecasts about the future of the economy or some aspect of it.
Applications in Business and Economics
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Data
Elements, Variables, and Observations Scales of Measurement Qualitative and Quantitative Data Cross-Sectional and Time Series Data
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Data and Data Sets
Data are the facts and figures that are collected, summarized, analyzed, and interpreted.
The data collected in a particular study are referred to as the data set.
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Elements, Variables, and Observations
The elements are the entities on which data are collected.
A variable is a characteristic of interest for the elements.
The set of measurements collected for a particular element is called an observation.
The total number of data values in a data set is the number of elements multiplied by the number of variables.
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Data, Data Sets, Elements, Variables, and Observations
Elements
Variables
Data Set Datum
Observation
Stock Annual Earn/Company Exchange Sales($M) Sh.($)Dataram AMEX73.10 0.86EnergySouth OTC 74.00 1.67Keystone NYSE 365.70 0.86 LandCare NYSE 111.40 0.33Psychemedics AMEX17.60 0.13
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Scales of Measurement
Scales of measurement include:• Nominal• Ordinal• Interval• Ratio
The scale determines the amount of information contained in the data.
The scale indicates the data summarization and statistical analyses that are most appropriate.
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Scales of Measurement
Nominal• Data are labels or names used to identify an
attribute of the element.• A nonnumeric label or a numeric code may
be used.
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Scales of Measurement
Nominal• Example:
Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on.
Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on).
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Scales of Measurement
Ordinal• The data have the properties of nominal
data and the order or rank of the data is meaningful.
• A nonnumeric label or a numeric code may be used.
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Scales of Measurement
Ordinal• Example:
Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.
Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).
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Scales of Measurement
Interval• The data have the properties of ordinal data
and the interval between observations is expressed in terms of a fixed unit of measure.
• Interval data are always numeric.
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Scales of Measurement
Interval• Example:
Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 points more than Kevin.
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Scales of Measurement
Ratio• The data have all the properties of interval
data and the ratio of two values is meaningful.
• Variables such as distance, height, weight, and time use the ratio scale.
• This scale must contain a zero value that indicates that nothing exists for the variable at the zero point.
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Scales of Measurement
Ratio• Example:
Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.
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Qualitative and Quantitative Data
Data can be further classified as being qualitative or quantitative.
The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.
In general, there are more alternatives for statistical analysis when the data are quantitative.
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Qualitative Data
Qualitative data are labels or names used to identify an attribute of each element.
Qualitative data use either the nominal or ordinal scale of measurement.
Qualitative data can be either numeric or nonnumeric.
The statistical analysis for qualitative data are rather limited.
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Quantitative Data
Quantitative data indicate either how many or how much.• Quantitative data that measure how many
are discrete.• Quantitative data that measure how much
are continuous because there is no separation between the possible values for the data..
Quantitative data are always numeric. Ordinary arithmetic operations are meaningful
only with quantitative data.
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Cross-Sectional and Time Series Data
Cross-sectional data are collected at the same or approximately the same point in time.• Example: data detailing the number of
building permits issued in June 2000 in each of the counties of Texas
Time series data are collected over several time periods.• Example: data detailing the number of
building permits issued in Travis County, Texas in each of the last 36 months
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Data Sources
Existing Sources• Data needed for a particular application
might already exist within a firm. Detailed information is often kept on customers, suppliers, and employees for example.
• Substantial amounts of business and economic data are available from organizations that specialize in collecting and maintaining data.
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Data Sources
Existing Sources• Government agencies are another important
source of data.• Data are also available from a variety of
industry associations and special-interest organizations.
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Data Sources
Internet• The Internet has become an important
source of data.• Most government agencies, like the Bureau
of the Census (www.census.gov), make their data available through a web site.
• More and more companies are creating web sites and providing public access to them.
• A number of companies now specialize in making information available over the Internet.
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Statistical Studies• Statistical studies can be classified as either
experimental or observational.• In experimental studies the variables of
interest are first identified. Then one or more factors are controlled so that data can be obtained about how the factors influence the variables.
• In observational (nonexperimental) studies no attempt is made to control or influence the variables of interest.• A survey is perhaps the most common
type of observational study.
Data Sources
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Data Acquisition Considerations
Time Requirement• Searching for information can be time
consuming.• Information might no longer be useful by
the time it is available. Cost of Acquisition
• Organizations often charge for information even when it is not their primary business activity.
Data Errors• Using any data that happens to be available
or that were acquired with little care can lead to poor and misleading information.
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Descriptive Statistics
Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.
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91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73
Example: Hudson Auto Repair
The manager of Hudson Auto would like to have
a better understanding of the cost of parts used in the
engine tune-ups performed in the shop. She examines
50 customer invoices for tune-ups. The costs of parts,
rounded to the nearest dollar, are listed below.
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Example: Hudson Auto Repair
Tabular Summary (Frequencies and Percent Frequencies) Parts Percent
Cost ($) Frequency Frequency 50-59 2 4 60-69 13 26 70-79 16 32 80-89 7 14 90-99 7 14 100-109 5 10
Total 50 100
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Example: Hudson Auto Repair
Graphical Summary (Histogram)
PartsCost ($)
2468
1012141618
Freq
uenc
y
50 60 70 80 90 100 110
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Example: Hudson Auto Repair Numerical Descriptive Statistics
• The most common numerical descriptive statistic is the average (or mean).
• Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50).
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Statistical Inference
Statistical inference is the process of using data obtained from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population).
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Example: Hudson Auto Repair
Process of Statistical Inference
1. Population consists of all
tune-ups. Averagecost of parts is
unknown.
2. A sample of 50engine tune-ups
is examined.
3. The sample data provide a sampleaverage cost of
$79 per tune-up.
4. The value of the sample average is usedto make an estimate of the population average.
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End of Chapter 1