Answer:
The range is defined as the difference between the term with the highest value and the term with the lowest value. This statistic is used to measure the variability of a series of data because it provides information on how far apart the values of a tail of the distribution are from the values at the other end of the tail.
Imagine that you manufacture a type of spare part for cars that must have a measurement of 10 cm with a margin of error of 1 cm.
This is:
10 ± 1 cm
Then you expect your manufacturing process to produce pieces with identical dimensions, that is, with little variability.
If you randomly select a sample of n pieces and measure them, the variability is expected to be low, so that your process is of quality, then expect a low range preferably less than 1 cm.
{10, 10.1, 10.5, 9.8, 9,6, 10.2} Range= 10.5 - 9.6 = 0.9 cm <em> low variability</em>
But if you find that the range is up to 8 cm, this would mean that not all pieces measure around 10 cm, it means that the variability of the measurements is high.
{14, 12, 11, 8, 7, 11, 12, 15} Range = 15 - 7 = 8 cm <em>high variability </em>
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