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? (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the standard deviation is 0.659 (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the variance is 0.429 (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the range is 6.360 (type an integer or decimal rounded to three decimal places as needed.) with the extra di (type an integer) with the extra di within 5 percentage points of each other, (type an integer) more than 5 percentage points apart. do the measure? choose the correct answer below the ranges are the variances are and the standard deviations are significantly

Explanation:

Step1: Recall the concept of significant change

We consider a change significant if it is more than 5 percentage points.

Step2: Analyze the given values

We are given that without the extra data - value, the range, variance and standard - deviation have certain values. With the extra data value, the range is 6.360. But we need to compare the variances and standard - deviations with the new data value to determine if there is a significant change. However, since the variance without the extra data value is 0.429 and we are not given the variance with the extra data value in the text (only the range with the extra data value is clearly stated), we assume we need to make a general judgment based on the range change. The range has changed. If we assume we had all the values for variance and standard - deviation with the extra data value, we would calculate the percentage change for each measure of variation. But since we don't have all the values, we can only say based on the range that the range has changed.

Answer:

The ranges are more than 5 percentage points apart, the variances are unknown, and the standard deviations are unknown.