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

range rule of thumb is the standard deviation is 1/4 of the range.

1/4 of the range 40 is 10 so that is the estimated standard deviation

percentage difference from actual standard deviation = (10.744-10)/10.744 * 100% = 6.925%

because the percentage difference is less than 15% the approximation is acceptable