What does the interquartile range tell you about the data?

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

The IQR is a useful statistic because it helps you understand the variability within a dataset by focusing on the central portion, which is less affected by extreme values or outliers. To calculate the IQR, you first need to find the first quartile (Q1) and the third quartile (Q3). The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half. The IQR is then found by subtracting Q1 from Q3 (IQR = Q3 - Q1).

For example, if you have a dataset of exam scores: 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, you would first find the median, which is 75. The lower half of the data is 55, 60, 65, 70, and the upper half is 80, 85, 90, 95, 100. The median of the lower half (Q1) is 65, and the median of the upper half (Q3) is 90. Therefore, the IQR is 90 - 65 = 25.

The IQR is particularly useful because it provides a measure of spread that is not influenced by outliers. This makes it a more reliable indicator of variability for skewed distributions or datasets with extreme values. By focusing on the middle 50% of the data, the IQR gives you a clearer picture of where the bulk of the data lies and how spread out it is.