use the magnitudes (richter scale) of the 120 earthquakes listed in the accompanying data - table. use…

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 of 1.95 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 four 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 four 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 correct answer. the range is , the variances are

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 of 1.95 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 four 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 four 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 correct answer. the range is , the variances are

Answer

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum

Step2: Recall variance formula

For a sample of data (x_1,x_2,\cdots,x_n), the sample - variance (s^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^{2}}{n - 1}), where (\bar{x}=\frac{\sum_{i=1}^{n}x_i}{n})

Step3: Recall standard - deviation formula

The sample - standard deviation (s=\sqrt{s^{2}})

Step4: Calculate without extra data value

First, find the maximum and minimum values in the original data set to calculate the range. Then, calculate the mean (\bar{x}), then ((x_i-\bar{x})^{2}) for each data point, 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 data value

Add the extra data value to the data set. Repeat the steps of finding the maximum and minimum for the range, calculating the mean, the squared differences, the variance, and the standard deviation.

Since the actual data values and the extra data value are not clearly readable in the provided image, we cannot perform the actual calculations. But the general steps for calculating range, variance, and standard deviation are as above.

If we assume we have the data set (x_1,x_2,\cdots,x_n) (without the extra value) and then (x_1,x_2,\cdots,x_n,x_{n + 1}) (with the extra value):

Let (x_{max}) and (x_{min}) be the maximum and minimum values of the data set without the extra value, and (X_{max}) and (X_{min}) be the maximum and minimum values of the data set with the extra value.

The range without the extra value (R_1=x_{max}-x_{min}) The range with the extra value (R_2=X_{max}-X_{min})

Let (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}) and (S_1^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^{2}}{n - 1}), (s_1=\sqrt{S_1^{2}}) be the variance and standard deviation without the extra value.

Let (\bar{X}=\frac{\sum_{i = 1}^{n}x_i+x_{n + 1}}{n + 1}), (S_2^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{X})^{2}+(x_{n + 1}-\bar{X})^{2}}{n}), (s_2=\sqrt{S_2^{2}}) be the variance and standard deviation with the extra value.

If the extra value is an outlier (either very large or very small compared to the original data set), the range, variance, and standard deviation are likely to change. If the extra value is close to the mean of the original data set, the changes may be small.

Answer:

Without performing actual calculations on the data (due to unreadable data in the image), we cannot provide numerical answers for the range, variance, and standard deviation with and without the extra data value. But the general method for calculation is as described above.