Question

Refer to the boxplots available below that are drawn on the same scale. One boxplot represents weights of​ men, and the other boxplot represents weights of women. Which boxplot represents weights of​ women? Explain.

Answer 1

Answer:

Considering that generally, men are heavier and bigger than women. The upper boxplot represents a more homogeneous group of men.  

Step-by-step explanation:

1) If we consider the boxplot below as the box and whiskers of the question. Then we can say that the Boxplot A (the first one):

A) The lowest weight: 50.3  The heaviest person weighs: 144.9 kg this group has a median of 84.4 kg. Also, the Interquartile Range of this distribution is given by :

$IIQ_{A}=Q_{3}-Q{1} \rightarrow IIQ_{A}=22.8$

First Quartile: 73, Second Quartile (Median): 84.4 and the Third Quartile: 95.8

$Q_{1}=73 \therefore 25\% \:of \:the \:distribution\:\leq 73\\Q_{2}=84.4 \therefore 50\% \:of \:the \:distribution\:\leq 84.4\\Q_{3}=95.8 \therefore 75\% \:of \:the \:distribution\:\leq 95.8$

2) Examining B:

B) The lowest weight of the distribution: 39 kg The heaviest person weighs: 150.4. This distribution has a median of 74 kg. And the Interquartile Range:

$IIQ_{B}=90.2-62.1=28.1$

First Quartile: 62.1, Second Quartile (Median): 74 and the Third Quartile: 90.2

$Q_{1}=62.1 \therefore 25\% \:of \:the \:distribution\:\leq 62.1\\Q_{2}=74 \therefore 50\% \:of \:the \:distribution\:\leq 74\\Q_{3}=90.2 \therefore 75\% \:of \:the \:distribution\:\leq 90.2$

3) So  considering,  all the data we can say:

1. The boxplot B is asymmetric to the left, most weights are closer to the lower values than the A.
2. The Interquartile range has 50% of the data, and the group B is thinner than the A. So $IIQ_{B}>IIQ_{A}$ while the B Distribution is more spread.
3. Considering that generally, men are heavier and bigger than women the upper boxplot could represent men.