### Topic Page: Range

**Range**

*Encyclopedia of Research Design*

The range of a distribution of values is the difference between the highest and lowest values of a variable or score. In other words, it is a single value obtained by subtracting the lowest (minimum) from the highest (maximum) value. Range provides an indication of statistical dispersion around the central tendency or the degree of spread in the data. There are several methods to indicate range, but most often it is reported as a single number, a difference score. However, in some contexts, the minimum and maximum are both presented to reflect the range as a pair of values. For example, if the data included values from 10 through 42, the range may be noted as either 32 (the difference between the highest and lowest value; i.e., 42 - 10) or the pair of numbers reflecting the lowest and highest values (10, 42).

The range is the smallest number subtracted from the largest number.

Example 1: What is the range of the following data set (1, 2, 3, 4, 2, 3, 4, 5, 5, 5)?

Range is 5 - 1 =4; otherwise noted as (1,5).

Example 2: What is the range of the following data set (1, 1, 1, 1, 1, 1, 1, 1, 1, 5)?

Range is 5 - 1 =4.

Example 3: What is the range of the following data set (1, 1, 1, 2, 2, 2, 2, 2, 10)?

Range is 10 - 1=9.

Range is typically used to characterize data spread. However, since it uses only two observations from the data, it is a poor measure of data dispersion, except when the sample size is large. Note that the range of Examples 1 and 2 earlier are both equal to 4. However, the two data sets contain different frequencies of each value. It is an unstable marker of variability because it can be highly influenced by a single outlier value, such as the value 10 in Example 3. One way to account for outliers is to artificially restrict the data range. A common method is to adjust the ends or extremes of the distribution curve. Typically, interquartile range (i.e., the distance between the 25th and 75th percentiles) is used. By definition, this contains 50 % of the data points in a normally distributed data set. In some contexts, it may be appropriate to use the semi-interquartile range, which covers 25% of the data points and is even less subject to variation due to scatter. Likewise, interdecile range evaluates only the 1st and 9th deciles or spread between 10th and 90th percentiles. This is similar to the median concept.

In correlational studies (examining how one variable relates to another), the sampling procedure, or the measuring instrument itself, sometimes leads to a restriction in the range of either or both of the variables being compared. The following examples illustrate the point.

The height of professional basketball players is more restricted than height in the general population.

The IQ scores of college seniors are more restricted than the IQ scores of the general population.

The vocabulary test scores of fifth graders are more restricted than the vocabulary test scores of all grade school children.

Tests that are extremely easy or difficult will restrict the range of scores relative to a test of intermediate difficulty. For example, if the test is so easy that everyone scores above 75%, the range of scores will obviously be less than a test of moderate difficulty in which the scores range from 30% to 95%.

Data that are restricted in range may produce a threat to interpretation of outcomes because they artificially reduce the size of the correlation coefficient. This is because restriction of range would be reflected in a smaller variance and standard deviation of one or both marginal distributions. For example, consider the use of height of basketball players to predict performance, as measured by points scored. Who is likely to score more, a person 62 inches (157.5 cm) tall or a person 82 inches (208.3 cm) tall? Nothing is certain, but a person who is 82 inches tall seems a better bet than someone 62 inches tall. Compare this situation with the question, Who is likely to score more, a person 81 inches (205.7 cm) tall or a person 82 inches tall? Here the prediction is much less certain. Predicting from the narrow range of 1 inch (2.54 cm) is extremely difficult compared with predicting from a range of 20 inches (50.8 cm). In sum, range restriction likely results in smaller variance, which in turn reduces the correlation coefficient.

Other references to range include the following:

Crude range: the difference between the highest and lowest score, another term commonly used for range.

Potential crude range: a potential maximum or minimum that will emanate from a measurement scale.

Observed crude range: the actual smallest and greatest observation that resulted from a measurement scale.

Midrange: the point halfway between the two extremes. It is an indicator of the central tendency of the data. Much like the range, it is not robust with small sample size.

Studentized range distribution: range has been adjusted by dividing it by an estimate of a population standard deviation.

Central Tendency, Measures of, Coefficients of Correlation, Alienation, and Determination, Correlation, Descriptive Statistics, Sample Size, “Validity”

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