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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.

1.36
1.49
1.09
0.96
1.32
1.27
0.79
1.19
1.41
0.52
0.55

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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 construct a boxplot and identify the 5-number summary from the given radiation absorption rates, we first need to sort the data in ascending order:

The given data points:

  • 1.36
  • 1.49
  • 1.09
  • 0.96
  • 1.32
  • 1.27
  • 0.79
  • 1.19
  • 1.41
  • 0.52
  • 0.55

Step 1: Sort the Data

The sorted data in ascending order is:

  • 0.52
  • 0.55
  • 0.79
  • 0.96
  • 1.09
  • 1.19
  • 1.27
  • 1.32
  • 1.36
  • 1.41
  • 1.49

Step 2: Determine the 5-Number Summary

The 5-number summary consists of the following:

  1. Minimum
  2. First quartile (Q1)
  3. Median (Q2)
  4. Third quartile (Q3)
  5. Maximum

Minimum:

  • The minimum value is the smallest number in the data: 0.52

Maximum:

  • The maximum value is the largest number in the data: 1.49

Median (Q2):

  • Since there are 11 data points, the median is the middle value, which is the 6th value in the sorted list:
  • Median (Q2) = 1.19

First Quartile (Q1):

  • The first quartile is the median of the first half of the data (the first 5 values):
  • First half: 0.52, 0.55, 0.79, 0.96, 1.09
  • Q1 is the median of these values (3rd value): 0.79

Third Quartile (Q3):

  • The third quartile is the median of the second half of the data (the last 5 values):
  • Second half: 1.19, 1.27, 1.32, 1.36, 1.41, 1.49
  • Q3 is the median of these values (3rd value): 1.36

Step 3: Compile the 5-Number Summary

Putting it all together, the 5-number summary is:

  • Minimum: 0.52
  • Q1: 0.79
  • Median (Q2): 1.19
  • Q3: 1.36
  • Maximum: 1.49

Final Answer

The 5-number summary is:

  • 0.52, 0.79, 1.19, 1.36, and 1.49 (in W/kg).