Question

use the range rule of thumb to approximate the standard deviation of the given data. 15, 42, 53, 7, 9, 12, 14, 28, 47 a. 15.8 b. 16.6 c. 11.5 d. 29.1

Explanation:

Step1: Find the range

The range \(R\) is calculated as \(R=\text{Max}-\text{Min}\).
Given data: \(15,42,53,7,9,12,14,28,47\).
\(\text{Max} = 53\), \(\text{Min}=7\).
\(R = 53 - 7=46\).

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

The range - rule - of - thumb formula for standard deviation \(s\) is \(s\approx\frac{R}{4}\).
Substitute \(R = 46\) into the formula: \(s\approx\frac{46}{4}=11.5\).

Answer:

C. 11.5