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 (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the standard deviation is (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the variance is (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.) with the extra data value, the standard deviation is (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the variance is (type an integer or decimal rounded to three decimal places as needed.) do the measures of variation change much with the extra data value? choose the the ranges are the variances are

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   (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the standard deviation is   (type an integer or decimal rounded to three decimal places as needed.) without the extra data value, the variance is   (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.) with the extra data value, the standard deviation is   (type an integer or decimal rounded to three decimal places as needed.) with the extra data value, the variance is   (type an integer or decimal rounded to three decimal places as needed.) do the measures of variation change much with the extra data value? choose the the ranges are   the variances are

Accepted Answer

# Explanation: ## Step1: Define range formula Range = Max - Min ## Step2: Define variance formula $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$ ## Step3: Define standard - deviation formula $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$ ## Step4: Calculate without extra value Using statistical software (e.g., Excel, R, Python's numpy and scipy.stats), input the 120 earthquake magnitude values. Calculate the maximum and minimum values to get the range. Calculate the mean $\bar{x}$, then the squared - differences $(x_{i}-\bar{x})^{2}$, sum them up, and divide by $n - 1$ to get the variance. Take the square - root of the variance to get the standard deviation. ## Step5: Calculate with extra value Add the value 7.00 to the data set (now $n=121$). Repeat the above steps for range, variance, and standard deviation calculations. ## Step6: Compare Compare the range, variance, and standard deviation values before and after adding the extra value to determine if the measures of variation change much. # Answer: Without the extra data value: Range: Standard deviation: Variance: With the extra data value: Range: Standard deviation: Variance: Do the measures of variation change much?

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Question

Explanation:

Step1: Define range formula

Step2: Define variance formula

Step3: Define standard - deviation formula

Step4: Calculate without extra value

Step5: Calculate with extra value

Step6: Compare

Answer: