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4. Introduction to Statistics Descriptive Statistics

Statistics for Engineers 4-1 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation to another. For example, the units might be headache sufferers and the variate might be the time between taking an aspirin and the headache ceasing. An observation or response is the value taken by a variate for some given unit. There are various types of variate. Qualitative or nominal; described by a word or phrase ( blood group, colour). Quantitative; described by a number ( time till cure, number of calls arriving at a telephone exchange in 5 seconds). Ordinal; this is an "in-between" case. Observations are not numbers but they can be ordered ( much improved, improved, same, worse, much worse). Averages etc. can sensibly be evaluated for quantitative data, but not for the other two.

Comparing mean, median and mode Symmetric data: the mean median and mode will be approximately equal. Skew data: the median is less sensitive than the mean to extreme observations. The mode ignores them. 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1 .0 1 .1 0 2 0 1 0 0 Re a ction time (s e c) F r e q u e n y His to g ra m o f re a c tio n time s ...

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4. Introduction to Statistics Descriptive Statistics

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Statistics for Engineers 4-6 Sample median The median is the central value in the sense that there as many values smaller than it as there are larger than it.

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