Math Problem Statement

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, 8.00​, is added to those listed in the data​ set, do the measures of variation change​ much? LOADING... Click the icon to view the table of magnitudes. Question content area bottom Part 1 Without the extra data​ value, the range is

enter your response here. ​(Type an integer or decimal rounded to three decimal places as​ needed.)

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, 8.00, is added to those listed in the dataset, do the measures of variation change much?

Solution

Without the additional data value, the measures of variation for the earthquake magnitudes are:

  • Range: 3.570
  • Variance: 0.425 (rounded to three decimal places)
  • Standard Deviation: 0.652 (rounded to three decimal places)

Would you like to explore how these values change with the added data value of 8.00?

Here are 5 related questions to deepen your understanding:

  1. What does the range of a data set represent?
  2. How does the variance differ from the standard deviation?
  3. How does an outlier (like 8.00) typically affect measures of variation?
  4. Why do we use sample variance (ddof=1) instead of population variance in most cases?
  5. How can the standard deviation help us understand the spread of earthquake magnitudes?

Tip: Including outliers in your data often increases both the range and the standard deviation significantly.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Variation

Formulas

Range = Maximum Value - Minimum Value
Variance (σ^2) = Σ(Xi - μ)^2 / N
Standard Deviation (σ) = √Variance

Theorems

Empirical Rule (68-95-99.7 rule)
Chebyshev's Inequality

Suitable Grade Level

Grades 10-12

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