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(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data.
4,8,8,6,2,9,8,7,9,6,9,5,1,6,2,9,8,7,7,9

min = 
Q1 = 
Q2 = 
Q3 = 
Max = 


 

The five number statistics are the minimum, the First Quartile (Q1), The median (Q2), the third Quartile (Q3) and the maximum value. 

To get this, arrange the data in ascending order;-  1 2 2 4 5 6 6 6 7 7 7 8 8 8 8 9 9 9 9 9

The minimum is 1 and the maximum is 9. 

To get the first quartile of any data, multiply 0.25 by the number of observations.  0.25 * 20 =  5, which means the first quartile is the average of the 5th and the 6th value.  25th percentile = (6+6)/2 = 6. 

The second quartile is the median, obtained by multiplying 0.5 by the number of values, 0.5 * 20 = 10. The median is the average of the 10th and the 11th value. Median = (7+7)/2 = 7. 

The third Quartile, 0.75 * 20 = 15.  The third quartile is the average of the 15th and the 16th value. 

3rd = (8+9)/2 =  8.5. 

Therefore, the five-number summary statistics are ;- 1, 6, 7,8.5 and 9

 

The Box plot is B

 

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