Question

the depths (in inches) at which 10 artifacts are found are listed. complete parts (a) and (b) below. 24.8 28.7 22.4 40.6 46.9 30.7 30.8 25.8 32.5 37.6 (a) find the range of the data set. range = 24.5 (round to the nearest tenth as needed.) (b) change 46.9 to 58.4 and find the range of the new data set. range = (round to the nearest tenth as needed.)

Explanation:

Step1: Find the maximum and minimum values in the new data set

The new data set is \(24.8, 28.7, 22.4, 40.6, 58.4, 30.7, 30.8, 25.8, 32.5, 37.6\).
The minimum value \(x_{\text{min}}=22.4\) and the maximum value \(x_{\text{max}} = 58.4\).

Step2: Calculate the range

The formula for the range \(R\) of a data set is \(R=x_{\text{max}}-x_{\text{min}}\).
Substitute \(x_{\text{max}} = 58.4\) and \(x_{\text{min}}=22.4\) into the formula: \(R = 58.4-22.4\).
\(R=36.0\)

Answer:

\(36.0\)