Question

what is the approximate ratio of the difference in means to the mads of the data sets?

Explanation:

Step1: Calculate the difference in means

The mean of Robin is \(107\) and the mean of Evelyn is \(138\). The difference in means is \(138 - 107=31\).

Step2: Calculate the sum of MADs

The MAD of Robin is \(5.2\) and the MAD of Evelyn is \(5.6\). The sum of MADs is \(5.2 + 5.6 = 10.8\).

Step3: Calculate the ratio

The ratio of the difference in means to the sum of MADs is \(\frac{31}{10.8}\approx 3\). Wait, no, wait the problem says "ratio of the difference in means to the MADs of the data sets". Wait, maybe it's \(\frac{\vert\overline{x}_1-\overline{x}_2\vert}{MAD_1 + MAD_2}\). But if we assume it's \(\frac{\vert138 - 107\vert}{5.2+5.6}=\frac{31}{10.8}\approx 3\). But wait, maybe there was a mis - understanding. If it's \(\frac{\vert\overline{x}_1-\overline{x}_2\vert}{\frac{MAD_1 + MAD_2}{2}}\) (average of MADs). The average of MADs is \(\frac{5.2 + 5.6}{2}=\frac{10.8}{2}=5.4\). Then \(\frac{31}{5.4}\approx 6\).

Answer:

\(6\)