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 is added to the data - set, do the measures of variation change much?

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 standard - deviation formula

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. However, since we are using technology, we can directly input the data (120 + 1 = 121 data values including the extra value) into a statistical software (e.g., Excel: STDEV.S function, R: sd() function, TI - 84 Plus: 1 - Var Stats).

Step2: Input data into technology

Input the 121 magnitudes (the 120 original magnitudes and the extra value) into the appropriate statistical function of the technology tool.

Answer:

(The actual value will depend on the technology used to calculate. If using Excel with the data in cells A1:A121, the formula =STDEV.S(A1:A121) will give the result. Without performing the actual calculation in a specific software, we can't provide the exact numerical answer. But the process is as described above.)