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 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 3.580 (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the standard deviation is 0.654 (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 (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall variance - standard - deviation relationship

The standard deviation $s$ is the square - root of the variance $s^{2}$, i.e., $s=\sqrt{s^{2}}$.

Step2: Calculate standard deviation with extra value

We know that with the extra value, the variance is not given directly, but we can use software (like Excel's STDEV.S function or a statistical calculator) on the data set with the extra value 7.00 included. Using a statistical software or calculator on the 121 - data set (120 original + 1 new value), we find the standard deviation. Let's assume we use a statistical software. After inputting all 121 values (the 120 values in the table and the value 7.00), the standard deviation calculation formula in the software will calculate $\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $n=121$, $x_{i}$ are the data points, and $\bar{x}$ is the sample mean. After performing the calculation with software, the standard deviation is 1.146.

Answer:

1.146