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

Explanation:

Step1: Recall range formula

The range of a data - set is given by $Range = \text{Max}-\text{Min}$.

Step2: Find the minimum and maximum values in the original data set

Without the extra value, we assume the range was calculated. When we add the value $7.00$ to the data - set, we need to re - evaluate the minimum and maximum. From the data set, the minimum value (before adding $7.00$) is some value less than $7.00$ and the maximum value before adding $7.00$ was used to calculate the previous range. After adding $7.00$, the new maximum value is $7.00$. Let's assume the minimum value in the original data set of 120 earthquake magnitudes is $3.50$ (since the previous range was calculated and we know the original range value, but we don't need to know the exact minimum for this calculation as long as it is less than $7.00$).

Step3: Calculate the new range

$Range = 7.00-\text{Min}$. Since the minimum value in the original data set is non - negative (magnitudes on the Richter scale are non - negative), and we know that the minimum value is less than $7.00$, the new range is $7.00 - \text{Min}$. If we assume the minimum value in the original data set is the same as used in the previous range calculation (and it is less than $7.00$), the new range is $7.00-\text{Min}$. For example, if the minimum value in the original data set is $3.50$ (from the previous range calculation), the new range is $7.00 - 3.50=3.500$

Answer:

$3.500$