Math Problem Statement

Use the magnitudes​ (Richter scale) of the earthquakes listed in the data set below. Find the mean and median of this data set. Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier​ (data value that is very far away from the​ others) when considered in the context of the sample data given in this data​ set? Explain. 2.78 2.09 0.42 2.45 1.44 2.06 2.07 0.28 0.21 0.64 2.12 2.18 1.84 1.98 1.16 2.06 2.78 1.87 0.37 0.92 0.35 0.21 2.24 0.42 0.06 1.29 1.65 2.11 2.77 2.75 2.34 2.83 2.79 0.61 1.77 0.87 0.85 1.06 1.55 1.03 1.55 0.05 1.74 0.33 2.67 1.64 2.57 0.39 0.93 1.86

Solution

The mean magnitude of the earthquakes is approximately 1.501.50, and the median is 1.6451.645.

To determine if an earthquake with a magnitude of 7.0 is an outlier, we calculated the interquartile range (IQR). The lower bound for potential outliers is approximately −1.45-1.45, and the upper bound is 4.264.26. Since 7.0 is significantly greater than 4.264.26, it is considered an outlier.

In summary, an earthquake measuring 7.0 on the Richter scale is an outlier in the context of this data set.

Would you like further details or have any other questions?

Here are 5 related questions to consider:

  1. How is the interquartile range (IQR) used to detect outliers?
  2. What is the difference between the mean and median, and why might they differ?
  3. How does the presence of outliers affect the mean and median of a data set?
  4. What is the significance of the lower and upper bounds in outlier detection?
  5. How could you handle outliers when analyzing a data set?

Tip: The median is often more robust to outliers than the mean, as extreme values can heavily influence the mean.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency
Outlier Detection

Formulas

Mean = (Sum of all values) / (Number of values)
Median = Middle value of ordered data set
Interquartile Range (IQR) = Q3 - Q1
Outlier bounds = [Q1 - 1.5 * IQR, Q3 + 1.5 * IQR]

Theorems

Interquartile Range (IQR) method for outlier detection

Suitable Grade Level

Grades 9-11

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