4.8:
Range Rule of Thumb to Interpret Standard Deviation
The range rule of thumb is a statistical tool to understand and interpret the standard deviation.
For a known standard deviation, the range rule can roughly estimate the maximum and minimum typical or usual values of that dataset.
It is based on the principle that ninety-five percent of all dataset values lie within two standard deviations from the mean.
Consider the marks scored by students with a mean of fifty and a standard deviation of fifteen. Using the formula, the minimum and maximum typical scores can be roughly predicted as 20 and 80. This indicates that marks scored by the majority of students would fall between 20 and 80. Anything less or more than this range is considered an outlier.
Conversely, using the known range of a dataset, one can estimate an unknown standard deviation. For instance, if the range of exam scores is known, then the standard deviation can be estimated by dividing the range by four.
Despite its simplicity, the range rule of thumb occasionally fails to predict outliers in a given dataset.
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.