how can the difference in the medians from these two years be expressed? a it is half of the interquartile…

Explanation:

Step1: Recall median - IQR relationship

In a box - and - whisker plot, the length of the box represents the inter - quartile range (IQR) and the line inside the box represents the median. If we assume some standard properties of box - and - whisker plots and the relationship between median differences and IQR. In a symmetric distribution, the distance from the median to the first or third quartile is half of the IQR. If we consider the change in medians between two years in terms of the box - and - whisker plot features, we know that the difference in medians can be related to the IQR. Let's assume the box - and - whisker plots for the two years. If we observe the structure of the box (IQR) and the position of the median within the box. When we compare the medians of two box - and - whisker plots, we note that if the change in medians is such that it is equivalent to a certain fraction of the IQR. In a well - behaved distribution, the difference in medians can be related to the IQR of one of the distributions. If we assume that the distribution of data for one of the years has a property such that the shift in the median is related to the spread of the middle 50% of the data (IQR). Usually, if the data has a certain symmetry or relative consistency in its spread, the difference in medians can be half of the IQR of one of the years. Looking at the box - and - whisker plots for the two years, we can see that the difference in medians is half of the inter - quartile range for this year.

Answer:

A. It is half of the interquartile range for this year.