Chapter XIV: Fundamentals of Probability and Statistics *

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1 Objectives Chapter XIV: Fudametals o Probability ad Statistics * Preset udametal cocepts o probability ad statistics Review measures o cetral tedecy ad dispersio Aalyze methods ad applicatios o descriptive statistics Review basic probability distributios. Fudametals o Probability ad Statistics A uderstadig o the udametals o probability ad statistics is basic to describig ad iterpretig data. This kowledge is also most valuable i dealig with radom evets ad risk which is iheret i busiess cotiuity plaig. Probability is a measure o the likelihood o occurrece o a evet. It could reer to the chace that a ew machie will work or ot; or the chace that a hurricae will occur; or the chace that a eighborhood will be hit by a heavy sow-storm. There are several ways o calculatig probability, ad we will eplore them later i this chapter. Statistics is the techique used to collect, describe ad aalyze data. For eample, i order to estimate the lie epectacy o a machie, oe ca collect the time-to-ailure o a umber o similar machies ad compute the average time-to ailure. This measure, average, becomes a statistic. It gives oe a idea o how log a machie will last. It is also possible to obtai the rage o values or the lie epectacy o a machie. The rage will give us a idea o the miimum ad maimum values. Such measures as average, rage ad may other measures are kow as statistics. We will develop several other statistics i this chapter. I the study o statistics, there are two basic cocepts that are crucial the cocept o populatio ad the cocept o sample. A populatio is the etity that we are iterested i studyig. However, it is usually ot advisable to collect data o whole populatios due to cost ad time cosideratios. ormal practice is to take a sample rom the populatio. The data collected rom the sample is used to develop sample characteristics kow as statistics. This will the be used to make iereces about the populatio characteristics kow as parameters. Data Classiicatio Discrete variables are variables whose outcomes are couted, or eample, the umber o requests or emergecy respose per day. Cotiuous variables are variables whose outcomes are measured, or eample, the time it takes to respod to a emergecy call. * Chapter prepared by Ore A. Soluade, PhD.

2 omial measuremets have o meaigul rak order amog values, or eample, the classiicatio o a weather evet as a torado, hurricae, or witer storm. Ordial measuremets have imprecise diereces betwee cosecutive values, but have a meaigul order to those values, or eample, the classiicatio o a torado as EF, EF, EF3, EF4, or EF5. Iterval measuremets have meaigul distaces betwee measuremets deied, but have o meaigul zero value deied, or eample, degrees Fahreheit. Ratio measuremets have both a zero value deied ad the distaces betwee dieret measuremets deied, or eample, loss measured i dollars. Graphical Presetatio o Data Oe powerul way o describig data is by displayig it o a chart. With the aid o Microsot Ecel, there are several optios or displayig data graphically, depedig o what iormatio oe is iterested i highlightig. For a set o discrete data, oe type o graphical represetatio is a bar chart. A eample o a bar chart is show i the igure below:

3 A lie graph displays iormatio as a series o data poits coected by straight lie segmets. Lie graphs are particularly revealig i there is tred i the data, as illustrated i the igure below: Stem ad Lea Plot A stem ad lea plot is a graphical display o the data that lists them i ascedig order ad the displays the distributio withi a give category. This is used as a prelimiary descriptio o the data beore more detailed aalysis is doe. Assume we have the ollowig set o data o the legth o time (i miutes) o power outages i a city i the last year, already sorted as ollows: A stem-ad-lea plot o this set o data is as show below: As ca be see, there are 3 data values i the tees, 3 data values i the tweties, i the thirties, 3 i the orties, i the ities, ad i the sities. 3

4 Frequecy Distributios Frequecy distributio is a tabular summary o a data set showig the umber o occurreces o each value or each class. This is true or both qualitative as well as quatitative data. Give the ollowig data: The correspodig requecy distributio is as show below: Measures o Cetral Tedecy Frequecy Measures o cetral tedecy o a set o data iclude the mea, the media, ad the mode. The mea is the average value, the media is the middle value, ad the mode is the value that occurs most requetly. There are two types o meas populatio mea, ad sample mea. Populatio Mea, is give by: μ 3 i i where i = the value o the i th item ad = populatio size. Sample mea,, is give by: where = sample size. 3 i i 4

5 Whe workig with data that is summarized i a requecy distributio comprisig classes o data, the computatio o the mea o the distributio is calculated usig the ormula: 33 3 i i i i i where i = requecy cout or i. Quartiles ad Percetiles Quartiles are used to split a dataset ito our equal parts. Oe ca determie the lowest 5% o the data as values below the irst quartile, the lowest 50% o the data as values below the secod quartile (also kow as the media), ad the lowest 75% o the data as values below the third quartile. The p th percetile is a value such that p percet o the data are below this value. Cotiued Copyright (c) 0 Kurt J. Egema ad Douglas M. Hederso. This is a ecerpt rom the book Busiess Cotiuity ad Risk Maagemet: Essetials o Orgaizatioal Resiliecy, ISB Rothstei Associates Ic., publisher (io@rothstei.com). See This ecerpt may be used solely i the evaluatio o this tetbook or course adoptio. It may ot be reproduced or distributed or used or ay other purpose without the epress permissio o the Publisher.