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Let's begin by analyzing the data to determine if there are any outliers.

The given data is:

12, 23, 56, 61, 45, 21, 10, 72, 26, 28, 54, 95, 43, 23, 12, 25, 74, 56, 64, 36, 39, 12.

To check for outliers, we can use the Interquartile Range (IQR) method:

1. **Order the data** from smallest to largest.
2. **Find the median (Q2)**, the first quartile (Q1), and the third quartile (Q3).
3. **Calculate the IQR** = Q3 - Q1.
4. Identify any data points that are outside the range defined by:
   - **Lower bound** = Q1 - 1.5 * IQR.
   - **Upper bound** = Q3 + 1.5 * IQR.
   Any data points outside this range are considered outliers.

Let me compute the steps and check if there are any outliers. numpy as np

# Given data
data = [12, 23, 56, 61, 45, 21, 10, 72, 26, 28, 54, 95, 43, 23, 12, 25, 74, 56, 64, 36, 39, 12]

# Sort the data
sorted_data = np.sort(data)

# Calculate the quartiles
Q1 = np.percentile(sorted_data, 25)
Q3 = np.percentile(sorted_data, 75)

# Calculate the IQR
IQR = Q3 - Q1

# Calculate the bounds
lower_bound = Q1 - 1.5 * IQR
upper_bound = Q3 + 1.5 * IQR

# Find outliers
outliers = [x for x in sorted_data if x < lower_bound or x > upper_bound]
outliers, lower_bound, upper_bound, Q1, Q3, IQRBased on the analysis using the Interquartile Range (IQR) method, there are **no outliers** in the given data.

Here are the key results:
- First Quartile (Q1): 23
- Third Quartile (Q3): 56
- Interquartile Range (IQR): 33
- Lower Bound: -26.5
- Upper Bound: 105.5

Since all data points fall within the range of -26.5 to 105.5, there are no outliers.

Would you like more details on this process, or do you have any further questions? Here are a few related questions to explore:

1. How do you calculate the median and other quartiles from a data set?
2. What is the effect of skewed data on the identification of outliers?
3. What are other methods to detect outliers besides IQR?
4. How can data transformation help in dealing with outliers?
5. How do outliers affect statistical measures like the mean and standard deviation?

**Tip:** If your data contains a large number of values, using a graphical method like a boxplot can provide a quick visualization of potential outliers.

Determine whether the following data has outliers: 12, 23, 56, 61, 45, 21, 10, 72, 26, 28, 54, 95, 43, 23, 12, 25, 74, 56, 64, 36, 39, 12

Learn how to determine outliers in a data set using the Interquartile Range (IQR) method. In this example, the data set includes values like 12, 23, 56, and 61. This process involves calculating the first and third quartiles, determining the IQR, and identifying data points outside the calculated bounds.

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