Questions: Construct a box plot from the given data. Use the approximation method Diameters of Cans in an Assembly Line: 5.5, 5.2, 5.7. 5.1, 5.5, 5.7, 5.8, 5.5, 5.8

Construct a box plot from the given data. Use the approximation method Diameters of Cans in an Assembly Line: 5.5, 5.2, 5.7. 5.1, 5.5, 5.7, 5.8, 5.5, 5.8
Transcript text: Construct a box plot from the given data. Use the approximation method Diameters of Cans in an Assembly Line: 5.5, 5.2, 5.7. 5.1, 5.5, 5.7, 5.8, 5.5, 5.8
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Solution

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Solution Steps

Step 1: Identify the Data

The given data set is: 5.3, 5.3, 5.3, 5.4, 5.4, 5.5, 5.5, 5.6, 5.6, 5.8.

Step 2: Arrange the Data in Ascending Order

The data is already arranged in ascending order: 5.3, 5.3, 5.3, 5.4, 5.4, 5.5, 5.5, 5.6, 5.6, 5.8.

Step 3: Calculate the Five-Number Summary
  • Minimum: The smallest value in the data set is 5.3.
  • First Quartile (Q1): The median of the first half of the data set. The first half is 5.3, 5.3, 5.3, 5.4, 5.4. The median of this subset is 5.3.
  • Median (Q2): The median of the entire data set. The middle values are 5.4 and 5.5, so the median is (5.4 + 5.5) / 2 = 5.45.
  • Third Quartile (Q3): The median of the second half of the data set. The second half is 5.5, 5.5, 5.6, 5.6, 5.8. The median of this subset is 5.6.
  • Maximum: The largest value in the data set is 5.8.

Final Answer

The five-number summary is:

  • Minimum: 5.3
  • First Quartile (Q1): 5.3
  • Median (Q2): 5.45
  • Third Quartile (Q3): 5.6
  • Maximum: 5.8
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