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 (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Find the maximum and minimum values

Using a statistical - software or calculator (e.g., in Excel, we can use the MAX and MIN functions), for the given 120 earthquake magnitudes data set. Let the maximum value be $M_{max}$ and the minimum value be $M_{min}$.

Step2: Calculate the range

The formula for the range $R$ is $R = M_{max}-M_{min}$.

Step3: Calculate the variance

The formula for the sample variance $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$, where $x_{i}$ are the individual data - points, $\bar{x}$ is the sample mean, and $n$ is the number of data - points. In software like Excel, we can use the VAR.S function.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^{2}}$. In Excel, we can use the STDEV.S function.

Step5: Add the new value and recalculate

Add the value 7.00 to the data set. Then repeat steps 1 - 4 to see how the range, variance, and standard deviation change.

Answer:

Without performing the actual calculations using software (since the problem asks to use technology), we cannot provide the exact numerical values. But the general procedure to find the range, variance, and standard deviation for the initial data set and then for the data set with the added value is as described above. To find the range without the extra data value, first identify the maximum and minimum values in the 120 - data - point set and subtract the minimum from the maximum.