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By Ishiguro M., Sakamoto Y.

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More surprisingly (perhaps), there are several competing measures, each with its own advantages and disadvantages. An obvious measure is the straightforward arithmetic average, given by adding up all the sample values and dividing by the number of these values. 2. 2 33 34 Populations, Samples and Data Summary This is usually termed the mean of the sample. 142. The mean is easily calculated and does indeed point at the centre of the data. However, an unsatisfactory feature is that it is very inﬂuenced by extreme values.

Presumably the particular examiner is important, and probably the test circuit. Maybe also the day of the week, as road conditions might vary from day to day. But how about weather? Or the time of day? Or any number of other such factors? The problem is that inclusion of more and more conditions reduces the number of previous occasions that match them, thereby reducing the number of test occasions for the calculation. Estimating a probability from small numbers of occasions leads to volatility: one instance more or less than the number observed can produce big swings in the proportions.

Various measurements are taken on each camshaft, one of them being the camshaft length. 2. Even though this is not a large sample by present-day standards, nevertheless, there are far too many numbers here for easy assimilation by eye and some condensation is needed. Can these 100 numbers be replaced by just a few well-chosen summary measures from which the main features of the whole sample can be gleaned? If it can, what should be the nature of these summary measures? If a single summary measure is sought in place of the whole collection of numbers then arguably the most important value is the position of the ‘centre’ of the data, as this value focuses attention on the approximate ‘location’ of the data.