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 3.590 (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 0.429 (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the range is 6.360 (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 the formula for standard - deviation.

The standard deviation $\sigma=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}}$ for a population and $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$ for a sample. In practice, we use technology (e.g., a statistical software like Excel, R, or a graphing calculator) to calculate it.

Step2: Enter the data (120 original data points + 1 new data point, 7.50) into the technology.

Let's assume we use a statistical software. We input all 121 data - points.

Step3: Use the software's function to calculate the standard deviation.

Most statistical software has built - in functions to calculate the standard deviation. For example, in Excel, we can use the STDEV.S function for a sample.

Answer:

(You need to actually use software like Excel, R, or a graphing calculator to input the 121 data - points and get the value. Since the original data is not fully entered here in a machine - readable format, we can't give the exact numerical answer. But the process above shows how to find it.)