numbers in the series differ from the average. The range is the difference between the smallest and largest values. The series can also be divided into four quartiles and the dispersion stated as the Coefficient of variation - x 100 (1.9) Skewness 1/5 Skewness 1.6.2 Permutations The distribution shown in Figure 1.4 is symmetrical since the mean, Combinations do not indicate any sequencing. When sequencing median and mode all coincide. Figure 1.5 shows a skewed distribu- within each combination is involved, the result is known as a tion with positive skewness. If the distribution bulges the other way, permutation. Therefore the number of permutations of two letters the skewness is said to be negative. out of four letters A, B, C, D is 12, i.e. AB, BA, AC, CA, AD, DA, There are several mathematical ways for expressing skewness. BC, CB, BD, DB, CD, DC. The number of permutations of r items They all give a measure of the deviation between the mean, median from a group of n is given by Equation 1.15. "P,-(n-r) (1.15) Mediam Regression and correlation 1.7.1 Regression Regression is a method for establishing a mathematical relationship Circuit errors between two variables. Several equations may be used to determine this relationship, the most common being that of a straight line. Figure 1.6 shows the number of defective public telephones which Figure 1.5 Illustration of skewness were reported at seven instances in time. This is called a scatter diagram. The points can be seen to lie approximately on the straight line AB. and mode and they are usually stated in relative terms for ease of comparison between series of different units. The Pearson coeffi- cient of skewness is given by Equation 1.10. Pr = Standard deviation = (1.10) Since the mode is sometimes difficult to measure this can also be stated as in Equation 1.11. Pt - 3(mean-median) (1.11) standard deviation Combinations and permutations 1.6.1 Combinations Combinations are the number of ways in which a proportion can be Figure 1.6 A scatter diagram chosen from a 