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Listed below are the measured radiation absorption rates​ (in W/kg) corresponding to 11 cell phones. Use the given data to construct a boxplot and identify the​ 5-number summary.

1.37
0.74
1.04
1.21
1.49
1.01
0.99
1.17
1.44
0.55
0.86

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Part 1
The​ 5-number summary is
  
enter your response here​,
  
enter your response here​,
  
enter your response here​,
  
enter your response here​, and
  
enter your response here​, all in​ W/kg.
​(Use ascending order. Type integers or decimals. Do not​ round.)

1 answer

To find the 5-number summary, we first need to organize the data in ascending order and then determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

Step 1: Organize the Data

Given data:

  • 1.37
  • 0.74
  • 1.04
  • 1.21
  • 1.49
  • 1.01
  • 0.99
  • 1.17
  • 1.44
  • 0.55
  • 0.86

Sorted in ascending order:

  • 0.55
  • 0.74
  • 0.86
  • 0.99
  • 1.01
  • 1.04
  • 1.17
  • 1.21
  • 1.37
  • 1.44
  • 1.49

Step 2: Determine the 5-Number Summary

  1. Minimum: 0.55
  2. Q1 (First Quartile): The first quartile is the median of the lower half of the data (excluding the overall median when the number of data points is odd). The lower half is:
    • 0.55, 0.74, 0.86, 0.99, 1.01 Median of this lower half = 0.86 (3rd value of the lower half).
  3. Median (Q2): The median is the middle value of the ordered dataset:
    • 1.04 (6th value in the ordered list).
  4. Q3 (Third Quartile): The third quartile is the median of the upper half of the data. The upper half is:
    • 1.17, 1.21, 1.37, 1.44, 1.49 Median of this upper half = 1.37 (3rd value of the upper half).
  5. Maximum: 1.49

5-Number Summary

  • Minimum: 0.55
  • Q1: 0.86
  • Median (Q2): 1.04
  • Q3: 1.37
  • Maximum: 1.49

Final Answer

The 5-number summary is:

  • 0.55,
  • 0.86,
  • 1.04,
  • 1.37,
  • 1.49 (all in W/kg).