Question

The double box and whisker plot shows the goals scored per game by two soccer teams during a 25 game season express the difference in the measures of center as a multiple of the measure of variation the difference between the Marians is times that I QR

Answer 1

the difference in median is 4/3 times the IQR

Explanation:

The median for team A = 4

The median for Team B = 8

The difference in median = median for Team B - median for Team A

The difference in median = 8 - 4

The difference in median = 4

The interquartile range (IQR) for team A = upper quartile - lower quartile

The interquartile range (IQR) for team A = Q3 - Q1 = 5 - 2

The interquartile range (IQR) for team A = 3

The interquartile range (IQR) for team B = upper quartile - lower quartile

The interquartile range (IQR) for team B = Q3 - Q1 = 9 - 6

The interquartile range (IQR) for team B = 3

Comparing the difference in median and the interquartile range:

difference in median: the interquartile range = 4:3

$\begin{gathered} \frac{difference\text{ in median}}{In\text{terquartle range}}=\frac{4}{3} \\ difference\text{ in median = }\frac{4}{3}\times In\text{terquartle range} \end{gathered}$

The differnce in median = 4/3 × IQR = 4/3 × 3 = 4

Hence, the difference in median is 4/3 times the IQR