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 (type an integer or decimal rounded to three decimal places as needed.) magnitudes 3.31 2.78 2.81 1.97 1.68 2.52 2.44 3.41 3.97 1.61 2.89 1.60 2.58 3.95 2.50 2.46 1.83 2.19 2.46 2.99 2.91 2.34 2.00 3.03 2.76 3.85 2.94 2.09 1.85 2.32 2.39 3.44 3.44 1.50 2.53 1.48 2.22 3.10 2.29 3.21 1.97 1.03 2.38 2.96 2.61 1.50 2.14 2.34 1.92 2.68 2.89 1.81 3.64 2.60 1.44 3.61 3.12 2.58 1.52 1.41 2.84 2.88 2.19 1.65 3.16 1.39 1.71 2.37 1.14 2.35 2.46 1.81 1.98 3.04 1.92 2.44 1.88 2.24 2.32 3.21 4.03 2.08 1.49 2.28 2.31 2.61 2.55 2.20 2.76 2.46 2.69 3.61 2.82 2.70 3.29 1.74 4.72 3.25 2.37 2.02 3.89 2.39 2.86 2.60 2.31 2.83 2.75 2.40 3.41 2.34 1.51 2.39 2.45 2.46 2.68 2.42 2.02 2.68 2.71 2.42

Explanation:

Step1: Recall formula for standard - deviation

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 number of data - points. In practice, we can use statistical software (e.g., Excel: STDEV.S function, R: sd() function, Python: numpy.std() with ddof = 1) to calculate it.

Step2: Calculate using technology

Using a statistical software or calculator with statistical functions, input the 120 earthquake magnitude values. For example, in Python:

import numpy as np
data = np.array([3.31, 2.78, 2.81, 1.97, 1.68, 2.52, 2.44, 3.41, 3.97, 1.61, 2.89, 1.60, 2.58, 3.95, 2.50, 2.46, 1.83, 2.19, 2.46, 2.99, 2.91, 2.34, 2.00, 3.03, 2.76, 3.85, 2.94, 2.09, 1.85, 2.32, 2.39, 3.44, 3.44, 1.50, 2.53, 1.48, 2.22, 3.10, 2.29, 3.21, 1.97, 1.03, 2.38, 2.96, 2.61, 1.50, 2.14, 2.34, 1.92, 2.68, 2.89, 1.81, 3.64, 2.60, 1.44, 3.61, 3.12, 2.58, 1.52, 1.41, 2.84, 2.88, 2.19, 1.65, 3.16, 1.39, 1.71, 2.37, 1.14, 2.35, 2.46, 1.81, 1.98, 3.04, 1.92, 2.44, 1.88, 2.24, 2.32, 3.21, 4.03, 2.00, 1.49, 2.28, 2.31, 2.61, 2.55, 2.20, 2.76, 2.46, 2.69, 3.61, 2.82, 2.70, 3.29, 1.74, 4.72, 3.25, 2.37, 2.02, 3.89, 2.39, 2.86, 2.60, 2.31, 2.83, 2.75, 2.40, 3.41, 2.34, 1.51, 2.39, 2.45, 2.46, 2.68, 2.42, 2.02, 2.68, 2.71, 2.42])
std = np.std(data, ddof = 1)

Answer:

0.584 (rounded to three decimal places)