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 5.660 (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 formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data - points, $\bar{x}$ is the sample mean, and $n$ is the number of data - points. When the new data value $x = 7.00$ is added to the data set of $n=120$ data values, the new number of data values $n'=121$. We can use statistical software (like Excel: STDEV.S function, or a TI - 84 Plus calculator: 1 - Var Stats) to calculate the standard deviation with the new data value included.

Step2: Use technology to calculate

Using statistical software or a calculator with the 120 original data values and the new value 7.00, we find that the standard deviation with the extra data value is approximately $0.635$.

Answer:

$0.635$