Which of the following expresses the distance between the medians as a multiple of the greater interquartile range?

Answer: To express the distance between the medians as a multiple of the greater interquartile range, we need to understand both terms.

Let's denote two medians as M1 and M2 (with M1 < M2 for simplicity). The "distance between the medians" is simply the difference between M2 and M1, which is calculated as M2 - M1.

Now, the interquartile range (IQR) is a measure of statistical dispersion and is the difference between the third quartile (Q3) and the first quartile (Q1) in a data set, which can be denoted as IQR = Q3 - Q1.

When we consider two different data sets or distributions, we need to find both of their interquartile ranges; let's call them IQR1 and IQR2. The "greater interquartile range" would be the larger of the two, which we can denote as max(IQR1, IQR2).

Finally, to express the distance between the medians as a multiple of the greater interquartile range, we divide the distance between the medians by the greater IQR. Mathematically:

Distance as multiple = (M2 - M1) / max(IQR1, IQR2)

The result tells us how many times the greater interquartile range fits into the distance between the medians. This comparison provides an idea of how spread out the distribution is in comparison to the difference in central tendency.