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 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 0.055 (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 8.360 (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.)

Explanation:

Step1: Recall standard - deviation formula

The standard deviation formula for a sample is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data - points, $\bar{x}$ is the sample mean, and $n$ is the sample size.

Step2: Use technology

We can use statistical software (like Excel, R, Python's numpy and scipy.stats libraries) or a graphing calculator to calculate the standard deviation. First, we input the 120 earthquake magnitudes from the table and then add the value 7.50 to the data - set.
Let's assume we use Python. We can use the following code:

import numpy as np
data = np.array([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, 2.90, 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, 1.49, 2.21, 3.07, 2.28, 3.20, 1.97, 1.90, 2.39, 2.01, 2.59, 1.49, 2.16, 2.34, 1.91, 2.73, 2.80, 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, 1.30, 1.75, 2.37, 1.14, 2.37, 2.48, 1.78, 2.00, 3.05, 1.93, 2.43, 1.80, 2.25, 2.36, 3.20, 4.01, 2.08, 1.50, 2.30, 2.31, 2.59, 2.57, 2.19, 2.76, 2.47, 2.73, 3.60, 2.84, 2.78, 3.26, 1.75, 4.73, 3.24, 2.30, 2.01, 3.85, 2.41, 2.87, 2.64, 2.33, 2.83, 2.74, 2.43, 3.42, 2.35, 1.51, 2.30, 2.42, 2.47, 2.07, 2.42, 2.78, 2.00, 2.70, 2.42, 7.50])
std = np.std(data, ddof = 1)
print(std)

When we run this code, we get the standard deviation.

Answer:

0.914 (rounded to three decimal places)