4.8: Range Rule of Thumb to Interpret Standard Deviation
The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height of the shortest and tallest student in that class can be calculated using the following formulae:
Height of the tallest student (maximum value) = mean + 2*s
Height of the shortest student (minimum value) = mean - 2*s
The tallest student has a height of 1.7 m, whereas the shortest student has a height of 1.5 m. So, one can conclude that the height of 95% of the students in the class falls within the range of 1.5 m to 1.7 m.
Additionally, from a range calculated from a known dataset, we can compute the standard deviation value. Consider an example of students’ test scores 80, 70, 50, 60, 90, 60, and 70. The dataset shows that the students’ scores lie within the range of 50-90. The minimum value is 50, and the maximum value is 90. The range of the student’s scores is 40. We can divide 40 by 4 to compute the standard deviation, s. For the above dataset, the standard deviation is 10.