Answer:
The is below
Step-by-step explanation:
To obtain the five-number summary, we need to find the minimum, maximum, median, and quartiles of the data set.
1. **Minimum**: The smallest value in the dataset is 323.
2. **Maximum**: The largest value in the dataset is 601.
3. **Median (Q2)**: To find the median, first arrange the data in ascending order:
323, 355, 380, 382, 389,
409,410 ,427 ,443 ,458 ,
465 ,471 ,475 ,478 ,480 ,
496 ,508 ,519
524525528531534537559565569574572585601
The middle value(s) are between positions (16 +1)/2 =8.5 and (17+1)/2=9
So Q2=(524+525)/2=524.5
4. **First Quartile (Q1)**: This is also known as lower quartile and represents the median of values below Q2.
For finding Q1:
Arrange all numbers from lowest to highest;
Find Median for Lower Half(Quartile)
In this case it will be average of position ((n/4)+((n/4)+1))/2 where n=32
So,Q1=((8+9)/2)=8.5
Therefore,Q1=(482+483)/2=482
5. **Third Quartile (Q3)**: This is also known as upper quartile and represents the median of values above Q3.
For finding Q3:
Arrange all numbers from lowest to highest;
Find Median for Upper Half(Quartile)
In this case it will be average of position (((n*3)/4)+(((n*3)/4)+1))/where n=32
So,Q3=((24+25))/24-25/26-27))=
Therefore,Q3=(558+559)/(26-27)=558
Therefore,the five-number summary for given data set would be:
Minimum:323
First Quartile(Q1):482
Median(Q2):524.5
Third Quartile(Q3):558
Maximum:601