If Xmin and Xmax 54 what is the range distribution What is

If X_min = ??? and X_max= 54 what is the range distribution? What is the purpose of the range for any given distribution?

Solution

the range of a set of data is the difference between the largest and smallest values.

However, in descriptive statistics, this concept of range has a more complex meaning. The range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. It is measured in the same units as the data. Since it only depends on two of the observations, it is most useful in representing the dispersion of small data sets

For a population, the range is greater than or equal to twice the standard deviation, which equality only for the coin toss (Bernoulli distribution with p = ½).

The range, in the sense of the difference between the highest and lowest scores, is also called the crude range. When a new scale for measurement is developed, then a potential maximum or minimum will emanate from this scale. This is called the potential (crude) range. Of course this range should not be chosen too small, in order to avoid a ceiling effect. When the measurement is obtained, the resulting smallest or greatest observation, will provide the observed (crude) range.

The midrange point, i.e. the point halfway between the two extremes, is an indicator of the central tendency of the data. Again it is not particularly robust for small samples.