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0, 39 Frequency Distributions FREQUENCY DISTRIBUTIONS A frequency distribution is formed by grouping the data into a number of classes or categories. The classes or categories are defined numerically, as in the following table . 9 Total 75 A frequency distribution summarises data; it does not provide the detailed information of an array, but is much easier to comprehend. 9 km contains more towns and villages than any other class. There is a progressive decline in frequencies either side of this, the class of highest frequency, or modal class .
It is this limiting value that constitutes the probabil ity of a black card. The " l ong run" definition of probability can be formalised as follows: the probability of a given event (or outcome) is the theoretical value of the proportion or fraction : Number of occurrences of the event Number of opportunities for occurrences of the event 30 Introduction to Statistics for Geographers and Earth Scientists when the number of opportunities is infinitely large. It is this definition that i s customarily employed in stat istical inference .
The probability of throwing either a 6 or a 1 with a single throw of a true die is 1/6 + 1/6 = 1/3. The probability of obtaining anyone of the four remaining numbers is 1/6 + 1/6 + 1/6 + 1/6 = 2/3. The probability of obtaining one of the six possible numbers is 1/3 + 2/3 = 1 . In general, if el, e2 , e3, . ,en are n mutually exclusive events having respective probabilities of occurrence PI, P2, P3, . ,Pn, the probability of either el or e2 occurring at anyone time is PI + P2, the probability of either el, e2 or e3 occurring is PI + P2 + P3, and the probability of one of the n separate events occurring is PI + P2 + P3 + •• .