Question

​(a) Find the​ five-number summary, and​ (b) draw a​ box-and-whisker plot of the data.

three

8  

8 

6

2 

9

8

7 

9  

6

9 

3 

2 

6 

2

9 

8 

7  

7

9

(a) min=__(simplify answer)

Q1=__ (simplify answer don't round)

Q2=___(simplify answer don't round)

Q3=__(simplify answer don't round)

max=___(simplify answer)

b) make correct box and whisker plot

Answer 1

The given data point is 8 8 6 2 9 8 7 9 6 9 3 2 6 2 9 8 7 7 9. Total no. of observation is 19.

A) Five number summary of these data as below:

Min= 2

Arrange the given data into ascending order, one will get 2 2 2 3 6 6 6 7 7 7 8 8 8 8 9 9 9 9 9

1/4*19=4.75 ~5. So, 5th observation in the sorted data gives 1st quartile. Hence, Q1=6

1/2*19=9.5 ~10. So, 10th observation in the sorted data gives 2nd quartile. Hence, Q2=7

3/4*19=14.25~14. So, 14th observation in the sorted data gives 3rd quartile. Hence, Q3=8

Max= 9

five number summary of the given data as follows (in R)

> x=c(8,8,6,2,9,8,7,9,6,9,3,2,6,2,9,8,7,7,9)
> fivenum(x)
[1] 2.0 6.0 7.0 8.5 9.0

B) Box & Whisker Plot of the given data as below:

> boxplot(x)