Question

use the data 1, 2, 3, 5, 6, 7. without actually computing the standard deviation, determine the value below that best approximates the standard deviation

choose the correct answer below.

○ a. 24
○ b. 2
○ c. 12
○ d. 6

Explanation:

Step1: Estimate the range

The range of the data \(1,2,3,5,6,7\) is \(R = 7 - 1=6\).

Step2: Use the range - rule - of - thumb

The range - rule - of - thumb states that \(s\approx\frac{R}{4}\) (for a sample). Substituting \(R = 6\) into the formula, we get \(s\approx\frac{6}{4}=1.5\). Another version of the range - rule - of - thumb is \(s\approx\frac{R}{2}\) (for a population, but this is less common). If we consider a more general rough estimate, values close to \(2\) are reasonable.

Answer:

B. 2