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 = 40

Standard Deviation = 10.744

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 40/4 = 10, so that is the estimate standard deviation

% error = (10.744-10)/10.744 * 100 = 6.925%, which would be acceptable.