otel Ltd BT Laboratories Mark Matthews Michael Talbot-Smith, BSc CPhys MInstP Northern Telecom Europe Independent Consultant Fraidoon Mazda, MPhil DFH DMS MBIM CEng FIEE Hugh Walker, BA (Cantab) MSc Northern Telecom Hewlett-Packard Ltd John McFarlane Samuel Welch, OBE MSc (Eng) CEng FIEE Northern Telecom Telecommunications Consultant Formerly Head of Signalling, BT S A Mohamed, BSc MSc PhD CEng MIEE BT Laboratories Phil Whiting University of Cambridge K L Moran, BSc (Hons) CEng MIEE Sprint International Hubert A J Whyte Newbridge Networks Ltd D G Morrison, MA Tim Williams, BSc CEng MIEE BT Laboratories ELMAC Services Richard J Mumford, CEng MIEE David J Withers, CEng FIEE Multitone Electronics plc Telecommunications Consultant This page intentionally left blank Statistical analysis Fraidoon Mazda MPhil DFH DMS MBIM CEng FIEE Northern Telecom Contents Introduction 1/3 Data presentation 1/3 Averages 1/3 Dispersion from the average 1/4 Skewness 1/5 Combinations and permutations 1/5 Regression and correlation 1/5 Probability 1/6 Probability distributions 1/7 Sampling 1/9 Tests of significance 1/10 Bibliography 1/11 This page intentionally left blank Introduction 1/3 1.1 Introduction Data are available in vast quantities in all areas of telecommunica- tions. This chapter describes the more commonly used techniques for presenting and manipulating data to obtain meaningful results. 1.2 Data presentation Probably the most common method used to present data is by tables and graphs. For impact, or to convey information quickly, picto- grams and bar charts may be used. Pie charts are useful in showing the different proportions of a unit. A strata graph shows how the total is split amongst its consti- tuents. For example, Figure 1.1 shows that the total revenue ob- Total revenue Age group Service A Figure 1.2 A histogram Service B Service C Service D "More than' Less than' curve Figure 1.1 Illustration of a strata graph tained by a PTO steadily increases with time, but that only services B and D have growth, whilst service C