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The following are the ratings of men by women in an experiment involving speed dating. Use the given data to construct a boxplot and identify the​ 5-number summary.

1.0
1.0
1.5
2.0
3.0
3.0
4.0
4.0
4.0
4.0
4.0
4.5
4.5
5.0
5.0
5.0
6.0
6.5
7.5
8.0

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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.
​(Use ascending order. Type integers or decimals. Do not​ round.)

1 answer

To find the 5-number summary (minimum, first quartile, median, third quartile, and maximum) for the given data, we'll follow these steps:

  1. Sort the Data: The data is already sorted in ascending order:

    1.0, 1.0, 1.5, 2.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.5, 4.5, 5.0, 5.0, 5.0, 6.0, 6.5, 7.5, 8.0

  2. Determine the Minimum and Maximum:

    • Minimum: 1.0
    • Maximum: 8.0

  3. Calculate the Median (Q2):

    • There are 20 data points (even number), so the median will be the average of the 10th and 11th values.
    • 10th value: 4.0
    • 11th value: 4.0
    • Median (Q2) = (4.0 + 4.0) / 2 = 4.0

  4. Calculate the First Quartile (Q1):

    • Q1 is the median of the first half of the data (the 1st to the 10th values).
    • First half: 1.0, 1.0, 1.5, 2.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0
    • Since there are 10 values in the first half (even), Q1 is the average of the 5th and 6th values.
    • 5th value: 3.0
    • 6th value: 3.0
    • Q1 = (3.0 + 3.0) / 2 = 3.0

  5. Calculate the Third Quartile (Q3):

    • Q3 is the median of the second half of the data (the 11th to the 20th values).
    • Second half: 4.5, 5.0, 5.0, 5.0, 6.0, 6.5, 7.5, 8.0
    • Since there are 10 values in the second half (even), Q3 is the average of the 5th and 6th values.
    • 5th value: 6.0
    • 6th value: 6.5
    • Q3 = (6.0 + 6.5) / 2 = 6.25

Now, compiling this information, the 5-number summary is:

  • Minimum: 1.0
  • Q1: 3.0
  • Median (Q2): 4.0
  • Q3: 6.25
  • Maximum: 8.0

Thus, the final 5-number summary can be written as:

The 5-number summary is
1.0,
3.0,
4.0,
6.25,
8.0.