**Arrange the Data:** Sort the dataset in ascending order.**Find the Quartiles:** Determine the lower quartile (Q1) and the upper quartile (Q3).**Subtract Q1 from Q3:** The difference between these quartiles is the IQR.

For example, in a dataset [2, 5, 6, 8, 12, 15, 18, 20, 22], Q1 is 6, and Q3 is 18. Therefore, the IQR is \( 18 – 6 = 12 \).

## The Importance of IQR in Data Analysis ๐

**Robustness to Outliers:** The IQR is less influenced by outliers or extreme values, making it a more reliable measure of spread for skewed distributions.**Focusing on the Core:** By concentrating on the middle 50%, the IQR provides a clearer picture of where the bulk of the data lies.**Comparative Analysis:** It’s particularly useful in comparing the spread of different datasets.

## Real-Life Applications of IQR ๐

**In Finance:** Analyzing the IQR of stock prices over a period can help investors understand typical market volatility.**In Real Estate:** The IQR of property prices in a neighborhood can give potential buyers a sense of the typical price range, excluding unusually high or low properties.**In Academia:** For test scores or research data, the IQR can highlight the range of typical outcomes, focusing on the majority rather than outliers.

## Visualizing the IQR: Box Plots and Beyond ๐

Box plots are an excellent tool for visualizing the IQR. They not only show the range of the middle 50% but also the median, highlighting the dataset’s central tendency alongside its variability.

## IQR: A Key Player in Outlier Detection ๐

The IQR is often used in identifying outliers. Data points that fall more than 1.5 times the IQR above Q3 or below Q1 are typically considered outliers, providing a quantifiable method to detect anomalous values.

**Example in Python**

Here is the code:

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For better understanding, run this code๐

# Creating the normal distribution data

normal_data = np.random.normal(100, 20, 200)

# Adding the outliers

data = np.append(normal_data, [300, 5])

# Create a line plot to visualize the data

plt.plot(data, marker=’o’, linestyle=’-‘)

plt.xlabel(‘Data Point’)

plt.ylabel(‘Value’)

plt.title(‘Line Plot of Data with Outliers’)

plt.grid(True) # Add grid lines for clarity

plt.show()

The Interquartile range (IQR) is robust for removing outliers.

Done

Very useful blog.

AOA, I found this blog to be a comprehensive and insightful explanation of the concept of IQR. This blog effectively defines IQR as a measure of spread that focuses on the middle 50% of a dataset, highlighting its significance in understanding data variability. It provides a step-by-step guide on calculating IQR and emphasizes its robustness to outliers, making it a reliable measure for skewed distributions. This blog also discusses the importance of IQR in data analysis, including its applications in finance, real estate, and academia. Furthermore, it introduces box plots as a visual tool for representing IQR and showcases an example in Python for outlier detection using IQR. It is a valuable read that deepened my understanding of IQR and its role in statistical analysis. ALLAH PAK ap ko dono jahan ki bhalian aata kry AAMEEN.