Develop the ability to find the five-number summary from actual data, draw a box-and-whisker plot, and compare and analyze the data.
Example ① (Comprehensive)
Test scores (10 students): 45, 52, 60, 63, 68, 72, 75, 80, 85, 92
(1) Find Q1, Q2, and Q3.
(2) Find the interquartile range and the range.
Answer: (1) Q2=(68+72)/2=70. Lower half 45,52,60,63,68 → Q1=60. Upper half 72,75,80,85,92 → Q3=80. (2) IQR=80−60=20. Range=92−45=47.
Test scores (10 students): 45, 52, 60, 63, 68, 72, 75, 80, 85, 92
(1) Find Q1, Q2, and Q3.
(2) Find the interquartile range and the range.
Answer: (1) Q2=(68+72)/2=70. Lower half 45,52,60,63,68 → Q1=60. Upper half 72,75,80,85,92 → Q3=80. (2) IQR=80−60=20. Range=92−45=47.
Key Points
- Always arrange the data in ascending order before calculating.
- Think in the order: five-number summary → box-and-whisker plot → reading and comparison.
Practice Problems
- Find the five-number summary of the data 12, 15, 18, 20, 25, 28, 30, 35, and calculate the IQR.
Answer and Explanation
- Answer: Minimum 12, Q1=(15+18)/2=16.5, Q2=(20+25)/2=22.5, Q3=(28+30)/2=29, maximum 35. IQR=29−16.5=12.5.