Answer: 9, 23, 26, 32, 48.
Explanation
To find the 5-number summary of this data we have to:
0. Determine the amount of numbers in the data set, which in our case is 25.
,1. Now, we have to organize from smallest to largest: 19, 20, 20, 21, 21, 23, 23, 24, 24, 24, 25, 25, 26, 27, 27, 29, 29, 30, 31, 33, 34, 35, 39, 42, 48.
,2. Next, we have to consider the 1st Quartile equation ¼ (n+1), median equation ½(n+1), and 3rd Quartile ¾(n+1).
,3. Now we have to consider the first number (19) and last number (48), and calculate the 1st, median and 3rd Quartile:
[tex]Q_1=\frac{1}{4}(25+1)=6.5[/tex][tex]Q_2=\frac{1}{2}(25+1)=13[/tex][tex]Q_3=\frac{3}{4}(25+1)=19.5[/tex]Therefore, based on the positions, the first quartile is until 23, the median is until 26, and the third is 32.
Finally, the 5-number summary is 19 (minimum), 23 (1st quartile), 26 (median), 32 (3rd quartile), 48 (maximum).
