Question

the 161 heights of males from a data set of body measurements vary from a low of 153.0 cm to a high of 191.2 cm. use the range rule of thumb to estimate the standard deviation s and compare the result to the standard deviation of 6.02 cm calculated using the 161 heights. what does the result suggest about the accuracy of estimates of s found using the range rule of thumb? assume the estimate is accurate if it is within 1.0 cm
use the range rule of thumb to estimate the standard deviation s.
( s=square ) cm
(type an integer or decimal rounded to two decimal places as needed)

Explanation:

Step1: Calculate the range

The range \(R\) is the difference between the maximum and minimum values.
\(R=\text{Max}-\text{Min}\)
Given \(\text{Max} = 191.2\) cm and \(\text{Min}=153.8\) cm.
\(R = 191.2-153.8=37.4\) cm.

Step2: Apply the range - rule - of - thumb formula

The range - rule - of - thumb formula for estimating the standard deviation \(s\) is \(s\approx\frac{R}{4}\).
Substitute \(R = 37.4\) into the formula:
\(s\approx\frac{37.4}{4}=9.35\) cm.

Answer:

The estimated standard deviation using the range rule of thumb is \(9.35\) cm.
Since the estimated value \(s = 9.35\) cm and the calculated value \(s=6.02\) cm, and \(|9.35 - 6.02|=3.33>1.0\), the estimate found using the range rule of thumb is not accurate (as the difference between the estimated and the actual standard deviation is more than \(1.0\)).