The Solution.
The five-number summary of any given set is referring to the Minimum value, lower quartile, median, upper quartile, and maximum value of the given data set.
First, we have to rearrange the data in ascending order of magnitude.
(a.) For the women:
[tex]20,22,24,27,28,31,32,36,40,43,44,46,47,48,52[/tex]The minimum value = 20
[tex]\text{Lower quartile =}\frac{1}{4}(N+1)th=(\frac{1}{4}\times16)th=4th=27[/tex][tex]Median\text{ =(}\frac{1}{2}N)th=(\frac{1}{2}\times15)th=7.5th=36[/tex][tex]Upp\text{er quartile =}\frac{3}{4}(N+1)th=(\frac{3}{4}\times16)th=(3\times4)th=12th=46[/tex]The maximum value = 52
(b.) For the men:
Re-arranging in ascending order, we get
[tex]30,32,34,35,38,40,43,46,49,52,54,56,57,60,63[/tex]The minimum value = 30
[tex]\text{Lower quartile =}\frac{1}{4}(N+1)th=(\frac{1}{4}\times16)th=4th=35[/tex][tex]Median\text{ =(}\frac{1}{2}N)th=(\frac{1}{2}\times15)th=7.5th=46[/tex][tex]Upp\text{er quartile =}\frac{3}{4}(N+1)th=(\frac{3}{4}\times16)th=(3\times4)th=12th=56[/tex]The maximum value = 63.