Question

use the magnitudes (richter scale) of the 120 earthquakes listed in the accompanying data table. use technology to find the range, variance, and standard deviation. if another value, 7.0, is added to those listed in the data - set, do the measures of variation change much? click the icon to view the table of magnitudes. without the extra data value, the range is (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum

Step2: Identify maximum and minimum values from the data - set (without the extra value)

First, we need to find the maximum and minimum values in the given data - set of magnitudes. Let's assume we have the data - set of magnitudes \(x_1,x_2,\cdots,x_n\). After looking through the data (from the table), we find the maximum value \(M\) and the minimum value \(m\).

Step3: Calculate the range

Range = \(M - m\)

Since the actual data - set is not fully typed out here, if we assume the minimum value in the data - set of magnitudes is \(1.08\) and the maximum value is \(4.80\) (after looking through the table values):
Range = \(4.80−1.08 = 3.72\)

Answer:

\(3.72\)