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. without the extra data value, the range is 3.590 (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.) magnitudes

Explanation:

Step1: Recall standard - deviation formula

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data - points, $\bar{x}$ is the sample mean, and $n$ is the sample size. We can use statistical software (e.g., Excel: STDEV.S function, R: sd() function, Python: numpy.std() with ddof = 1) to calculate it directly.
Let's assume we use a statistical software (e.g., Python with the following code):

import numpy as np
data = [3.28, 2.80, 2.83, 1.97, 1.69, 2.51, 2.45, 3.42, 3.97, 1.59, 2.88, 1.61, 2.55, 4.00, 2.53, 2.44, 1.83, 2.17, 2.43, 2.99, 2.89, 2.36, 2.00, 3.03, 2.76, 3.87, 2.94, 2.06, 1.84, 2.32, 2.38, 3.43, 3.42, 1.53, 2.56, 1.40, 2.21, 3.07, 2.28, 3.26, 1.97, 1.90, 2.39, 2.91, 2.59, 1.49, 2.16, 2.34, 1.91, 2.73, 2.89, 1.82, 3.67, 2.67, 1.44, 3.62, 3.12, 2.59, 1.54, 1.41, 2.85, 2.87, 2.18, 1.64, 3.19, 1.39, 1.75, 2.37, 1.14, 2.37, 2.48, 1.78, 2.00, 3.05, 1.93, 2.43, 1.86, 2.25, 2.36, 3.20, 4.01, 2.08, 1.50, 2.30, 2.31, 2.50, 2.57, 2.19, 2.76, 2.47, 2.73, 3.00, 2.84, 2.70, 3.26, 1.75, 4.73, 3.24, 2.39, 2.01, 3.85, 2.41, 2.87, 2.64, 2.33, 2.83, 2.74, 2.43, 3.42, 2.35, 1.51, 2.39, 2.42, 2.47, 2.67, 2.42, 2.78, 2.66, 2.70, 2.42]
s = np.std(data, ddof = 1)
print(s)

Answer:

0.624