Range

Examples of Range

[Page 1368]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.

Examples of Range Restriction

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.

• 1.
  The height of professional basketball players is more restricted than height in the general population.
• 2.
  The IQ scores of college seniors are more restricted than the IQ scores of the general population.
• 3.
  The vocabulary test scores of fifth graders are more restricted than the vocabulary test scores of all grade school children.
• 4.
  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%.