Descriptive StatisticsDescriptive statistics are methods for organizing and summarizing data. For example, tables or graphs are used to organize data, and descriptive values such as the average score are used to summarize data. A descriptive value for a population is called a parameter and a descriptive value for a sample is called a statistic.

Inferential StatisticsInferential statistics are methods for using sample data to make general conclusions (inferences) about populations. Because a sample is typically only a part of the whole population, sample data provide only limited information about the population. As a result, sample statistics are generally imperfect representatives of the corresponding population parameters.

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Typesof StatisticsTwo types of statistics:Descriptive Statistics:Describes the characteristics of a product or process using information collected on itInferential Statistics (Inductive):Draws conclusions on unknown process parameters based on information contained in a sample.Uses probability

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Use of statistics in businessAccountingPublic accounting firms use statistical sampling procedures when conducting audits for their clients.FinanceFinancial analysts 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.

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Use of statistics in businessProductionA 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.

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Data are whole set of numbers that represent the facts and figures that are collected, summarized, analyzed, and interpreted.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.

Basic Vocabulary Terms

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Qualitative dataQualitative 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.

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Quantitative dataQuantitative 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.

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

population and sampleThe population is the set of all elements of interest in a particular study.A sample is a subset of the population.A variable is a characteristic or condition that can change or take on different values. Types of variable :Qualitative and quantitative variable Types of qualitative variable :discrete and continuous

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

population and samplePopulations and Samples *PopulationSample

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

*Measuring variables To establish relationships between variables, researchers must observe the variables and record their observations. This requires that the variables be measured. The process of measuring a variable requires a set of categories called a scale of measurement and a process that classifies each individual into one category.

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

*Types of Measurement scaleA nominal scale is an unordered set of categories identified only by name. Nominal measurements only permit you to determine whether two individuals are the same or different.ex , Religion,color, GenderAn ordinal scale is an ordered set of categories. Ordinal measurements tell you the direction of difference between two individuals. Ex, Economic status

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

*Types of Measurement scale

3. An interval scale is an ordered series of equal-sized categories. Interval measurements identify the direction and magnitude of a difference. The concept of zero point is not included. Temperature, I.Q score4. A ratio scale is an interval scale where a value of zero indicates none of the variable. Ratio measurements identify the direction and magnitude of differences and allow ratio comparisons of measurements. Zero point is the absence of the characteristic. Ex, height

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Organizing and Presenting Data GraphicallyData in raw form are usually not easy to use for decision makingSome type of organization is neededTableGraphTechniques reviewed here:Bar charts and pie charts Pareto diagramOrdered arrayStem-and-leaf displayFrequency distributions, histograms and polygonsCumulative distributions and ogivesContingency tablesScatter diagrams

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Tables and Charts for Categorical DataCategorical DataGraphing DataPie ChartsPareto DiagramBar ChartsTabulating Data Summary Table

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

The Summary TableExample: Current Investment Portfolio

Investment Amount Percentage Type (in thousands $) (%)

Stocks 46.5 42.27

Bonds 32.0 29.09

CD 15.5 14.09

Savings 16.0 14.55

Total 110.0 100.0(Variables are Categorical)Summarize data by category

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Bar and Pie ChartsBar charts and Pie charts are often used for qualitative data (categories or nominal scale)

Height of bar or size of pie slice shows the frequency or percentage for each category

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Bar Chart ExampleInvestment Amount PercentageType (in thousands $) (%)

Stocks 46.5 42.27

Bonds 32.0 29.09

CD 15.5 14.09

Savings 16.0 14.55

Total 110.0 100.0Current Investment Portfolio

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Amount in $1000's

Investor's Portfolio

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Investment typesAmount in K$%

Stocks46.5

Bonds32

CD15.5

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Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Pie Chart ExamplePercentages are rounded to the nearest percentCurrent Investment Portfolio Savings 15%CD 14%Bonds 29%Stocks42%Investment Amount PercentageType (in thousands $) (%)

Stocks 46.5 42.27

Bonds 32.0 29.09

CD 15.5 14.09

Savings 16.0 14.55

Total 110.0 100.0

Chart1

42.2727272727

29.0909090909

14.0909090909

14.5454545455

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InvestmentInvestor AInvestor BInvestor C

Stocks46.55527.542.2727272727

Bonds32441929.0909090909

CD15.52013.514.0909090909

Savings1628714.5454545455

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Comparing Investors

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Investment typesPercentageCumulative

Stocks42.2742.27

Bonds29.0971.36

Savings14.5585.91

CD14.09100

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Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Pareto DiagramUsed to portray categorical data (nominal scale)A bar chart, where categories are shown in descending order of frequencyA cumulative polygon is often shown in the same graphUsed to separate the vital few from the trivial many

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Pareto Diagram Examplecumulative % invested (line graph)% invested in each category (bar graph)Current Investment Portfolio

Pareto

0.420.42

0.290.71

0.150.86

0.141

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Tables and Charts for Numerical DataNumerical DataOrdered ArrayStem-and-LeafDisplayHistogramPolygonOgiveFrequency Distributions andCumulative Distributions

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

The Ordered ArrayA sequence of data in rank order: Shows range (min to max) Provides some signals about variability within the range May help identify outliers (unusual observations) If the data set is large, the ordered array is less useful

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Data in raw form (as collected):

24, 26, 24, 21, 27, 27, 30, 41, 32, 38

Data in ordered array from smallest to largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41(continued)The Ordered Array

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Stem-and-Leaf DiagramA simple way to see distribution details in a data set

METHOD: Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves)

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

ExampleHere, use the 10s digit for the stem unit:Data in ordered array:21, 24, 24, 26, 27, 27, 30, 32, 38, 4121 is shown as38 is shown as41 is shown asStem Leaf 2 1 3 8 4 1

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

ExampleCompleted stem-and-leaf diagram:(continued)Data in ordered array:21, 24, 24, 26, 27, 27, 30, 32, 38, 41

StemLeaves21 4 4 6 7 730 2 841

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Using other stem unitsUsing the 100s digit as the stem:Round off the 10s digit to form the leaves

613 would become 6 1776 would become 7 8 . . .1224 becomes 12 2

Stem Leaf

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Using other stem unitsUsing the 100s digit as the stem:The completed stem-and-leaf display:

Stem Leaves(continued) 6 1 3 6 7 2 2 5 8 8 3 4 6 6 9 9 9 1 3 3 6 8 10 3 5 6 11 4 7 12 2Data:

613, 632, 658, 717,722, 750, 776, 827,841, 859, 863, 891,894, 906, 928, 933,955, 982, 1034, 1047,1056, 1140, 1169, 1224

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

What is a Frequency Distribution?A frequency distribution is a list or a table containing class groupings (ranges within which the data fall) ...and the corresponding frequencies with which data fall within each grouping or categoryTabulating Numerical Data: Frequency Distributions

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Why Use a Frequency Distribution?It is a way to summarize numerical dataIt condenses the raw data into a more useful form... It allows for a quick visual interpretation of the data

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Class Intervals and Class BoundariesEach class grouping has the same widthDetermine the width of each interval byUsually at least 5 but no more than 15 groupingsClass boundaries never overlapRound up the interval width to get desirable endpoints

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Frequency Distribution ExampleExample: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Sort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58Find range: 58 - 12 = 46Select number of classes: 5 (usually between 5 and 15)Compute class interval (width): 10 (46/5 then round up)Determine class boundaries (limits): 10, 20, 30, 40, 50, 60Compute class midpoints: 15, 25, 35, 45, 55Count observations & assign to classesFrequency Distribution Example(continued)

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Frequency Distribution Example

Class Frequency10 but less than 20 3 .15 1520 but less than 30 6 .30 3030 but less than 40 5 .25 25 40 but less than 50 4 .20 2050 but less than 60 2 .10 10 Total 20 1.00 100RelativeFrequency PercentageData in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58(continued)

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Tabulating Numerical Data: Cumulative FrequencyClass10 but less than 20 3 15 3 1520 but less than 30 6 30 9 4530 but less than 40 5 25 14 7040 but less than 50 4 20 18 9050 but less than 60 2 10 20 100 Total 20 100 PercentageCumulative PercentageData in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58FrequencyCumulative Frequency

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Graphing Numerical Data: The HistogramA graph of the data in a frequency distribution is called a histogram The class boundaries (or class midpoints) are shown on the horizontal axisthe vertical axis is either frequency, relative frequency, or percentage Bars of the appropriate heights are used to represent the number of observations within each class

Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Class MidpointsHistogram Example(No gaps between bars)Class10 but less than 20 15 320 but less than 30 25 630 but less than 40 35 540 but less than 50 45 450 but less than 60 55 2FrequencyClass Midpoint

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Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Graphing Numerical Data: The Frequency PolygonClass MidpointsClass10 but less than 20 15 320 but less than 30 25 630 but less than 40 35 540 but less than 50 45 450 but less than 60 55 2FrequencyClass Midpoint(In a percentage polygon the vertical axis would be defined to show the percentage of observations per class)

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Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon)Class Boundaries (Not Midpoints)ClassLess than 10 0 010 but less than 20 10 1520 but less than 30 20 4530 but less than 40 30 7040 but less than 50 40 9050 but less than 60 50 100Cumulative PercentageLower class boundary 10 20 30 40 50 60

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Basic Business Statistics, 10e 2006 Prentice-Hall, Inc.Chap 2-*

Side-by-Side Chart ExampleSales by quarter for three sales territories: