 is reducing and may event- ually become unprofitable. Figure 1.3 Illustration of ogives Logarithmic or ratio graphs are used when one is more interested in the change in the ratios of numbers rather than their absolute value. In the logarithmic graph, equal ratios represent equal dis- tances. (1.1) Frequency distributions are conveniently represented by a histo- gram as in Figure 1.2. This shows the number of people using a given service, banded according to age group. There are very few (1.2) users below 20 years and above 55 years, the most popular ages being 35 to 40 years. This information will allow the service pro- vider to target its advertising more effectively. In a histogram, the areas of the rectangles represent the frequen- cies in the different groups. Ogives, illustrated in Figure 1.3, show The arithmetic mean is easy to calculate and it takes into account the cumulative frequency occurrences above or below a given all the figures. Its disadvantages are that it is influenced unduly by value. From this curve it is possible to read off the total number of extreme values and the final result may not be a whole number, users above or below a specific age. which can be absurd at times, e.g. a mean of 2.5 men. 1.3.2 Median and mode 1.3 Averages Median or 'middle one' is found by placing all the figures in order 1.3.1 Arithmetic mean and choosing the one in the middle or, if there are an even number of items, the mean of the two central numbers. It is a useful The arithmetic mean of n numbers X1, X2, X3, Xn is given by technique for finding the average of items which cannot be ex- Equation 1.1 which is written as in Equation 1.2. pressed in figures, e.g. shades of a colour. It is also not influenced 1/4 Statistical analysis by extreme values. However, the median is not representative of all the figures. The mode is the most 'fashionable' item, that is, the one which Circuit A appears the most frequently. Average 1.3.3 Geometric mean Circuit B The geometric mean of n numbers X1, X2, X3, Xn is given by Equa