IntroductionDescriptive statistics involves thearrangement, summary, and presentation ofdata, to enable meaningful interpretation, and tosupport decision making.Descriptive statistics methods make use of graphical techniques numerical descriptive measures.The methods presented apply to both the entire population the population sample2.2 Types of data and informationA variable – a characteristic of population orsample that is of interest for us. Cereal choice Capital expenditure The waiting time for medical servicesData – the actual values of variables Interval data are numerical observations Nominal data are categorical observations Ordinal data are ordered categorical observations
Types of data and informationA variable – a characteristic of population orsample that is of interest for us. Cereal choice Capital expenditure The waiting time for medical servicesData – the actual values of variables Interval data are numerical observations Nominal data are categorical observations Ordinal data are ordered categorical observations
Types of data and informationA variable – a characteristic of population orsample that is of interest for us. Cereal choice Capital expenditure The waiting time for medical servicesData – the actual values of variables Interval data are numerical observations Nominal data are categorical observations Ordinal data are ordered categorical observations
Types of data – analysisKnowing the type of data is necessary to properlyselect the technique to be used when analyzing data.Type of analysis allowed for each type of data Interval data – arithmetic calculations Nominal data – counting the number of observation in eachcategory Ordinal data – computations based on an ordering processCross-Sectional/Time-Series DataCross sectional data is collected at a certainpoint in time Marketing survey (observe preferences by gender,age) Test score in a statistics course Starting salaries of an MBA program graduatesTime series data is collected oversuccessive points in time Weekly closing price of gold Amount of crude oil imported monthly2.3 Graphical Techniques forInterval DataExample 2.1: Providing informationconcerning the monthly bills of newsubscribers in the first month aftersigning on with a telephone company. Collect data Prepare a frequency distribution Draw a histogram
Relative frequencyIt is generally best to use equal class width,but sometimes unequal class width are calledfor.Unequal class width is used when thefrequency associated with some classes istoo low. Then, several classes are combined together to form awider and “more populated” class. It is possible to form an open ended class at thehigher end or lower end of the histogram.Class width
Example 2.2: Selecting an investment An investor is considering investing in oneout of two investments. The returns on these investments wererecorded. From the two histograms, how can theinvestor interpret the Expected returns The spread of the return (the risk involved witheach investment)
Example 2.2: Conclusion It seems that investment A is better, because: Its expected return is only slightly below that ofinvestment B The risk from investing in A is smaller. The possibility of having a high rate of return existsfor both investment.Providing informationExample 2.3: Comparing students’performance Students’ performance in two statistics classeswere compared. The two classes differed in their teachingemphasis Class A – mathematical analysis and development oftheory. Class B – applications and computer based analysis. The final mark for each student in each coursewas recorded. Draw histograms and interpret the results.Interpreting histograms
Graphical Techniques forNominal dataThe only allowable calculation on nominaldata is to count the frequency of each valueof a variable.When the raw data can be naturallycategorized in a meaningful manner, we candisplay frequencies by Bar charts – emphasize frequency of occurrencesof the different categories. Pie chart – emphasize the proportion ofoccurrences of each category.The Pie ChartThe pie chart is a circle, subdivided intoa number of slices that represent thevarious categories.The size of each slice is proportional tothe percentage corresponding to thecategory it represents.Example 2.4 The student placement office at a universitywanted to determine the general areas ofemployment of last year school graduates. Data was collected, and the count of theoccurrences was recorded for each area. These counts were converted to proportionsand the results were presented as a piechart and a bar chart.The Pie Chart
Describing the RelationshipBetween Two VariablesWe are interested in the relationship betweentwo interval variables.Example 2.7 A real estate agent wants to study the relationshipbetween house price and house size Twelve houses recently sold are sampled andthere size and price recorded Use graphical technique to describe therelationship between size and price
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