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.

Question

1.36
0.57
0.85
0.59
1.41
1.07
0.96
1.24
1.48
0.52
0.93

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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.)

Answer 1

To construct the 5-number summary and a boxplot, we first need to sort the given data in ascending order. The data provided is:

1.36, 0.57, 0.85, 0.59, 1.41, 1.07, 0.96, 1.24, 1.48, 0.52, 0.93

Step 1: Sort the Data

Sorting the data in ascending order:

• 0.52
• 0.57
• 0.59
• 0.85
• 0.93
• 0.96
• 1.07
• 1.24
• 1.36
• 1.41
• 1.48

Step 2: Calculate the 5-Number Summary

The 5-number summary consists of the following:

1. Minimum: The smallest value in the data set.
2. Q1 (First Quartile): The median of the lower half of the data (the 25th percentile).
3. Median (Q2): The median (the 50th percentile), which is the middle value.
4. Q3 (Third Quartile): The median of the upper half of the data (the 75th percentile).
5. Maximum: The largest value in the data set.

Minimum

• Minimum = 0.52

Q1

To find Q1, we look at the lower half of the data:

• Lower half: 0.52, 0.57, 0.59, 0.85, 0.93
• Q1 = Median of lower half = 0.59

Median (Q2)

• The median (middle value of the entire sorted list) is the average of the 6th and 7th values:
• Median = (0.96 + 1.07) / 2 = 1.015

Q3

To find Q3, we look at the upper half of the data:

• Upper half: 1.07, 1.24, 1.36, 1.41, 1.48
• Q3 = Median of upper half = 1.36

Maximum

• Maximum = 1.48

Final 5-Number Summary

So, the 5-number summary is:

• Minimum: 0.52
• Q1: 0.59
• Median (Q2): 1.015
• Q3: 1.36
• Maximum: 1.48

Conclusion

Thus, the 5-number summary is:

0.52, 0.59, 1.015, 1.36, 1.48 (in W/kg).