Question

the 150 heights of males from a data set of body measurements vary from a low of 156.0 cm to a high of 190.1 cm. use the range rule of thumb to estimate the standard deviation s and compare the result to the standard deviation of 10.21 cm calculated using the 150 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 1.2 cm.

use the range rule of thumb to estimate the standard deviation s.

s = □ 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 \(\text{Max} = 190.1\) cm and \(\text{Min}=156.0\) cm.
\(R = 190.1- 156.0=34.1\) 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 \(R = 34.1\) into the formula:
\(s\approx\frac{34.1}{4}=8.525\approx8.53\) cm.

Step3: Compare with the given standard deviation

The given standard deviation is \(s = 10.21\) cm.
The difference between the estimated value and the calculated value is \(|10.21 - 8.53|=1.68\) cm.

Answer:

The estimated standard deviation using the range rule of thumb is \(s = 8.53\) cm. Since the difference \(1.68>1.2\) cm, the estimate from the range rule of thumb is not accurate.