Understanding the Interquartile Range (IQR): A Statistical Measure for Data Spread and Outlier Detection

Interquatile Range (IQR)

The Interquartile Range (IQR) is a statistical measure that describes the spread or dispersion of data

The Interquartile Range (IQR) is a statistical measure that describes the spread or dispersion of data. It is based on the concept of quartiles, which divide a set of data into four equal parts.

To calculate the IQR, you need to find the first quartile (Q1) and the third quartile (Q3).

1. Arrange your data in ascending order.
2. Find the median (Q2). If the number of data points is odd, Q2 is the middle value. If the number of data points is even, Q2 is the average of the middle two values.
3. Split the data into two halves: the lower half (below Q2) and the upper half (above Q2).
4. Find the median of the lower half, which is the first quartile (Q1).
5. Find the median of the upper half, which is the third quartile (Q3).

The IQR is then calculated as the difference between Q3 and Q1: IQR = Q3 – Q1.

The IQR is useful in describing the spread of data because it focuses on the middle 50% of the values, ignoring any extreme outliers. This makes it more robust to outliers compared to other measures of spread, such as the range or standard deviation.

For example, let’s say we have the following dataset: 10, 12, 13, 15, 20, 22, 25, 28, 30, 35, 50.

1. Arranging the data in ascending order: 10, 12, 13, 15, 20, 22, 25, 28, 30, 35, 50.
2. Finding the median (Q2): 20.
3. Splitting the data into lower half: 10, 12, 13, 15 and upper half: 22, 25, 28, 30, 35, 50.
4. Finding the median of the lower half (Q1): 12.
5. Finding the median of the upper half (Q3): 28.

The IQR is calculated as: 28 – 12 = 16.

So, the IQR for this dataset is 16, indicating that the middle 50% of the values are spread out over a range of 16.

The IQR is often used in box plots, which visually display the spread and distribution of data. It can also be used to detect outliers by defining limits for mild and extreme outliers, commonly known as the “1.5 IQR rule.”

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