Final answer:
To approximate the standard deviation using the 'range divided by 4' rule, find the range of the data set and divide it by 4. In this case, the approximate standard deviation is 1.25.
Step-by-step explanation:
To approximate the standard deviation using the 'range divided by 4' rule, you need to find the range of the given set of sample data and divide it by 4. In this case, the range is the difference between the maximum and minimum values of the data set, which is 6 - 1 = 5. Dividing the range by 4 gives us 5/4 = 1.25. Therefore, the approximate standard deviation using this rule is 1.25.