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 3.580 (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 0.426 (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

Range = Maximum - Minimum

Step2: Find maximum and minimum with new value

From the data, the original maximum value among the 120 earthquake - magnitudes is less than 7.00. The minimum value remains the same. So, with the extra data value of 7.00, the new maximum is 7.00. Assume the minimum value in the original data set is \(x\).

Step3: Calculate new range

Let's assume the minimum value in the original data set is 1.41 (from the given data). Then the range with the extra data value is \(7.00 - 1.41=5.590\)

Answer:

5.590