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, 7.50, 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. 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 a value? choose the correct answer below. variations are more than 5 percentage points apart, and the standard deviations are more than 5 percentage points apart to significantly

Explanation:

Step1: Recall definitions

Range is the difference between the maximum and minimum values. Variance measures how far a set of numbers is spread out. Standard - deviation is the square - root of the variance.

Step2: Analyze effect of new value on range

The range is calculated as $R = \max(x_i)-\min(x_i)$. If a new value (7.50) is added, if this new value is greater than the current maximum or less than the current minimum, the range will change.

Step3: Analyze effect of new value on variance and standard - deviation

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

Answer:

All of them change