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. only the variance changes only the standard deviation changes only the range changes none of them change only the range and standard deviation change only the range and variance change only the variance and standard deviation change all of them change

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum. Adding a new value (7.00) will change the maximum value if it is the largest among all, thus changing the range.

Step2: Recall variance formula

$s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$. Adding a new data - point changes the mean $\bar{x}$ and the sum of squared deviations $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}$, so the variance will change.

Step3: Recall standard deviation formula

$s=\sqrt{s^{2}}$. Since the variance changes, the standard deviation (which is the square - root of the variance) will also change.

Answer:

all of them change