Ask a New Question
Menu

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
2.0
2.5
3.5
4.5
4.5
5.0
5.0
5.0
5.0
5.0
6.0
6.5
7.0
7.0
7.0
8.0
8.5
9.5
9.5

Question content area bottom
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 construct the 5-number summary from the given speed dating ratings, we first need to organize the data in ascending order:

Sorted Data: 1.0, 2.0, 2.5, 3.5, 4.5, 4.5, 5.0, 5.0, 5.0, 5.0, 5.0, 6.0, 6.5, 7.0, 7.0, 7.0, 8.0, 8.5, 9.5, 9.5

Five-Number Summary:

  1. Minimum: The smallest value in the dataset.
  2. First Quartile (Q1): The median of the first half of the dataset.
  3. Median (Q2): The median of the entire dataset.
  4. Third Quartile (Q3): The median of the second half of the dataset.
  5. Maximum: The largest value in the dataset.

Step-by-step calculation:

  1. Minimum: \( 1.0 \)

  2. Maximum: \( 9.5 \)

  3. Median (Q2):

    • There are 20 data points, so the median is the average of the 10th and 11th values.
    • 10th value: \( 5.0 \)
    • 11th value: \( 5.0 \)
    • \( \text{Median} = \frac{5.0 + 5.0}{2} = 5.0 \)

  4. First Quartile (Q1):

    • The first half of the data includes the first 10 values: \( 1.0, 2.0, 2.5, 3.5, 4.5, 4.5, 5.0, 5.0, 5.0, 5.0 \).
    • The median of this subset (5 values from either side) is the average of the 5th and 6th values:
    • 5th value: \( 4.5 \)
    • 6th value: \( 4.5 \)
    • \( Q1 = \frac{4.5 + 4.5}{2} = 4.5 \)

  5. Third Quartile (Q3):

    • The second half of the data includes the last 10 values: \( 5.0, 5.0, 6.0, 6.5, 7.0, 7.0, 7.0, 8.0, 8.5, 9.5 \).
    • The median of this subset (5 values from either side) is the average of the 5th and 6th values:
    • 5th value: \( 7.0 \)
    • 6th value: \( 7.0 \)
    • \( Q3 = \frac{7.0 + 7.0}{2} = 7.0 \)

5-Number Summary:

  • Minimum: 1.0
  • Q1: 4.5
  • Median (Q2): 5.0
  • Q3: 7.0
  • Maximum: 9.5

Final Answer:

The 5-number summary is \( 1.0, 4.5, 5.0, 7.0, 9.5 \).