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, 7.50, 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 3.560 (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the standard deviation is 0.655 (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the variance is 0.420 (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the range is 6.300 (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the standard deviation is 0.784 (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 the relationship between variance and standard - deviation

The variance $s^{2}$ is the square of the standard - deviation $s$. That is, $s^{2}=s\times s$.

Step2: Identify the standard - deviation with the extra data value

The standard deviation with the extra data value is $s = 0.764$.

Step3: Calculate the variance

We square the standard deviation. So, $s^{2}=(0.764)^{2}=0.584656\approx0.585$.

Answer:

$0.585$