Does the range rule of thumb produce an acceptable​ approximation? Suppose a researcher deems the approximation as acceptable if it has an error less than​ 15%.

Question

Below are the range and standard deviation for a set of data. Use the range rule of thumb and compare it to the standard deviation listed below. Does the range rule of thumb produce an acceptable​ approximation? Suppose a researcher deems the approximation as acceptable if it has an error less than​ 15%.

Range = 2.85

Standard Deviation = 0.955

The estimated standard deviation is _______.

​(Round to three decimal places as​ needed.)

Answer 1

the rule of thumb is that the range is 4 times the standard deviation (or the standard deviation is 1/4 of the range).

1/4 of the range here is 2.85/4 = 0.7125, so that is the estimate standard deviation

% error = (0.955-0.7125)/0.955 * 100 = 25.393%, which would not be acceptable.