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By Bouchaud J.-P.

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Extra resources for An introduction to statistical finance

Sample text

Discrete variables have exact values, like the number of subjects in an experiment. Continuous variables can take on any value, but the process of measurement always reduces them to discrete variables. Thus, measurement of a continuous variable gives us approximate values, like the length or weight of an object. When computations involve both approximate and exact numbers (as is typical in calculating an average), the approximate numbers dictate the accuracy of the outcome. Variables may be qualitative, expressing only differences in kind (nominal scale), or they may be quantitative, expressing differences in amount (ordinal, interval, and ratio scales).

These are examples of questions that we can answer more easily if we organize the distribution in cumulative form. A cumulative frequency distribution shows how many cases lie below the upper real limit of each class interval. 8. We start at the bottom and record for each class interval the total frequency of cases falling below its upper real limit. ) These figures appear in the fourth column, headed cum f. We obtain them by adding the frequency of the given class interval to the cumulative frequency recorded for the next lower class interval.

Thus, it could be better called an equal-interval scale. Examples of this type of scale are degrees of temperature on the Fahrenheit or Celsius scales. A 10° rise in a reading on the Celsius scale represents the same change in heat when going from 0° to 10° as when going from 20° to 30°. 1. The top of this illustration shows three temperatures in degrees Celsius: 0°, 50°, and 100°. It is tempting to think of 100°C as twice as hot as 50°. However, the value of zero on this scale is simply an arbitrary reference point (the freezing point of water) and does not imply an absence of heat.