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, 7.00, is added to those 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 3.580 (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the standard deviation is 0.054 (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the variance is 0.428 (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the range is 5.860 (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the standard deviation is 0.708 (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the variance is (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall variance - standard - deviation relationship

The variance $s^{2}$ is the square of the standard - deviation $s$.

Step2: Calculate variance with extra data value

Given the standard - deviation with the extra data value $s = 0.708$. Then the variance $s^{2}=(0.708)^{2}=0.499$.

Answer:

$0.499$