Question

Does the nature of the data allow you describe the difference of the two medians as a multiple of the interquartile range? If so, what is the multiple?

Answer 1

Yes, I can describe the difference of the two medians as a multiple of the interquartile range as shown below.

Explanation:

The difference of the medians for the two data sets is 69 − 60 = 9. The interquartile ranges for the data sets are 9 ounces and 8 ounces.

This shows that the difference of the medians is about 1 times, or nearly equal to, the interquartile range of either data set.

For Genivieve, the multiple is 1:

9 = m(9)

m = 1

For Mindy, the multiple is 1.125:

9 = m(8)

m = 1.125

(This is the answer on edumentum)

Answer 2

1/3

Explanation:

From the figure, we know that the median of Amy is 40 and the median of Megan is 35.

Therefore the difference in their medians is = 40 - 35

= 5

We see that Q1 of Megan is 25 and Q3 is 40. Therefore, her interquartile range is given by Q3 - Q1 = 40 - 25

= 15

So, the difference of the medians is the multiple of the interquartile range.

So the multiple is = 5/15

= 1/3 (IQR of Megan)