Calculate the IQR (to 4 decimal places) from the following list of values:
 
 
46, 47, 64, 44 ,54, 56, 58, 61, 50, 51, 46, 54, 53, 52, 34, 46
 

# Given list of values
values = [46, 47, 64, 44, 54, 56, 58, 61, 50, 51, 46, 54, 53, 52, 34, 46]

# Calculate Q1 (25th percentile) and Q3 (75th percentile)
Q1 = np.percentile(values, 25)
Q3 = np.percentile(values, 75)

# Calculate IQR
IQR = Q3 - Q1
IQR_rounded = round(IQR, 4)
IQR_roundedThe Interquartile Range (IQR) of the given list of values is **8.5000** (rounded to four decimal places).

Would you like to explore more about this calculation or have any other questions?

Here are some related questions:
1. What do Q1 and Q3 represent in a data set?
2. How does the IQR help in identifying outliers?
3. What is the difference between the IQR and the range of a dataset?
4. How would the IQR change if all values in the data set were increased by a constant?
5. Why is the IQR considered a robust measure of variability?

**Tip:** The IQR is often used to detect outliers. Values that lie below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR are typically considered outliers.

Learn how to calculate the Interquartile Range (IQR) from a given list of values with a step-by-step solution. This problem covers key concepts in descriptive statistics, including percentiles and the IQR formula. Suitable for students in Grades 9-12.

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