Summary  
This chapter demonstrates how to calculate the interquartile range by obtaining the 25th and 75th percentiles with a quantile function, derive upper and lower bounds using a threshold multiplier, and filter a dataset to detect and remove outliers.

General domain of usage  
Data preprocessing and cleaning

Another effective way to detect and remove outliers is by using the **interquartile range (IQR)** method.

## What Is IQR?
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as:

$$
IQR = Q3−Q1
$$

Where:
- $$Q1$$: 25th percentile (first quartile);
- $$Q3$$: 75th percentile (third quartile).

Values lying below $$Q1 − 1.5 \times IQR$$ or above $$Q3 + 1.5 \times IQR$$ are typically considered outliers.

## Calculating IQR
To calculate the IQR value and detect the outliers, you first need to know the 25th percentile and 75th percentile values. They can be obtained with the `quantile()` function. Then, you can compute the IQR value by following the formula.
```
q1_placement <- quantile(df$placement_exam_marks, 0.25)
q3_placement <- quantile(df$placement_exam_marks, 0.75)
iqr_placement <- q3_placement - q1_placement
```

## Identifying Outliers
Similar to the z-score method, you need to identify the lower and upper boundaries:
```
Thresh_hold <- 1.5
upper_boundary <- q3_placement + (Thresh_hold * iqr_placement)
lower_boundary <- q1_placement - (Thresh_hold * iqr_placement)
```

Then you can either select all outliers to analyze them:
```
df[df$placement_exam_marks > upper_boundary | df$placement_exam_marks < lower_boundary,]
```

Or create an outlier-free dataset:
```
df2 <- df[df$placement_exam_marks <= upper_boundary & df$placement_exam_marks >= lower_boundary,]
```

Gain practical experience in data analysis with R by learning how to clean, transform, and visualize datasets. Explore essential workflows such as selecting and filtering data, handling missing values, and summarizing results. Build confidence in preparing data for insights, reporting, and deeper statistical exploration.

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Strengthen your understanding of statistics for data analysis. Apply descriptive measures, identify and treat outliers, and use correlation techniques with visual tools like heatmaps and scatter plots to uncover meaningful relationships.

Removing Outliers Using IQR Method

What Is IQR?

Calculating IQR

Identifying Outliers