# NTERQUARTILE RANGE (IQR)

The IQR is the length of the box in a box plot. It is computed as

IQR = Q3 −Q1

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where Q1 and Q3 are the 25th and 75th percentiles.

What percent of the data fall between Q1 and the median? What percent is between the median and Q3?10

Extending out from the box, the whiskers attempt to capture the data outside of the box. However, their reach is never allowed to be more than 1.5× IQR. They capture everything within this reach. In the upper whisker does not extend to the last two points, which is beyond Q3 + 1.5× IQR, and so it extends only to the last point below this limit. The lower whisker stops at the lowest value, 5.31%, since there is no additional data to reach; the lower whisker’s limit is not shown in the figure because the plot does not extend down to Q1−1.5× IQR. In a sense, the box is like the body of the box plot and the whiskers are like its arms trying to reach the rest of the data.

Any observation lying beyond the whiskers is labeled with a dot. The purpose of labeling these points – instead of extending the whiskers to the minimum and maximum observed values – is to help identify any observations that appear to be unusually distant from the rest of the data. Unusually distant observations are called outliers. In this case, it would be reasonable to classify the interest rates of 24.85% and 26.30% as outliers since they are numerically distant from most of the data.