## Interquartile Range (IQR)

### The interquartile range (IQR) is a statistical measure that represents the dispersion or spread of a set of data

The interquartile range (IQR) is a statistical measure that represents the dispersion or spread of a set of data. It is specifically used to describe the middle 50% of the data, which is a more robust measure than the range.

To calculate the interquartile range, you first need to find the first quartile (Q1) and the third quartile (Q3) of the data set. The first quartile represents the 25th percentile or the value below which 25% of the data falls, while the third quartile represents the 75th percentile or the value below which 75% of the data falls.

Once you have identified Q1 and Q3, you calculate the interquartile range by subtracting Q1 from Q3: IQR = Q3 – Q1.

The IQR is useful in analyzing data sets that contain outliers or skewed distributions because it is less affected by extreme values. It provides a measure of the spread of the middle half of the data, which helps assess the variability and central tendency of the dataset more effectively than the range alone.

Moreover, the IQR can be used to identify outliers by using a rule known as the “1.5 * IQR rule.” According to this rule, any data point that falls below Q1 – 1.5 * IQR or above Q3 + 1.5 * IQR is considered an outlier.

In summary, the IQR is a statistical measure that quantifies the spread of the middle 50% of a dataset, making it a robust measure of variability. It is calculated by finding the difference between the third and first quartiles and is particularly useful for detecting outliers and describing data with skewed distributions.

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