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.

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Part 1

Find the mean and median of the data set using a calculator or similar data analysis technology.

The mean of the data set is 

enter your response here.

​(Round to three decimal places as​ needed.)

To help you find the mean and median of the earthquake data, you would typically need the full list of magnitudes provided in the data set. Since the data isn't included in your question, I'll explain the steps for calculating the mean and median of a dataset using a calculator or technology, as well as how to determine if 7.0 is an outlier.

### Steps for finding the **mean** and **median**:

1. **Mean**:
   - Add all the data values together.
   - Divide the total by the number of data points in the set.
   - Formula for the mean:  
     \[
     \text{Mean} = \frac{\sum x_i}{n}
     \]
     where \(x_i\) are the individual data points, and \(n\) is the number of data points.

2. **Median**:
   - Arrange the data in ascending order.
   - If the number of data points is odd, the median is the middle value.
   - If the number of data points is even, the median is the average of the two middle values.

### Steps to identify an **outlier**:
   - Calculate the interquartile range (IQR).
   - Formula for IQR:
     \[
     \text{IQR} = Q3 - Q1
     \]
     where \(Q1\) is the first quartile (25th percentile), and \(Q3\) is the third quartile (75th percentile).
   - Outliers typically lie outside the range:
     \[
     [Q1 - 1.5 \times \text{IQR}, Q3 + 1.5 \times \text{IQR}]
     \]
   - If 7.0 lies outside this range, it would be considered an outlier.

Once you provide the data points, I can help you with the calculations or walk you through the process further.

Would you like to upload the dataset or share the magnitudes for further analysis? Feel free to ask questions!

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### Related Questions:
1. How do you find quartiles and IQR in a dataset?
2. What does it mean for a value to be an outlier in the context of statistical data?
3. What is the significance of an earthquake’s magnitude on the Richter scale?
4. Can you explain how the median is affected by extreme values?
5. How would you calculate variance and standard deviation for this dataset?

### Tip:
When checking for outliers, always remember to check the IQR method for a more robust identification, especially when dealing with non-normally distributed data.

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.

Learn how to calculate the mean, median, and detect outliers in earthquake magnitude data using the Richter scale. This example guides you through finding central tendencies and identifying an outlier (7.0) using the Interquartile Range (IQR) method. Suitable for students in Grades 9-12.

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