What can you infer from the interquartile range?

The interquartile range (IQR) measures the spread of the middle 50% of a data set.

The IQR is a useful statistic in understanding the variability within a data set. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). The first quartile represents the 25th percentile, meaning 25% of the data points are below this value. The third quartile represents the 75th percentile, meaning 75% of the data points are below this value. By focusing on the middle 50% of the data, the IQR provides a measure of spread that is not affected by extreme values or outliers.

For example, if you have a data set of exam scores, the IQR can help you understand how spread out the middle range of scores is. If the IQR is small, it means that the middle 50% of students scored similarly, indicating consistency. If the IQR is large, it suggests a wider range of scores among the middle 50%, indicating more variability.

The IQR is particularly useful when comparing different data sets. For instance, if you are comparing the exam scores of two different classes, the IQR can help you determine which class has more consistent performance. A smaller IQR in one class compared to another suggests that the scores in that class are more tightly clustered around the median.

In summary, the IQR is a valuable tool for understanding the spread and consistency of the central portion of a data set, making it easier to analyse and compare different sets of data.