#14
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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#14
![### Educational Resource on Five-Number Summary and Box-and-Whisker Plot
#### Problem Statement
(a) **Give the five-number summary for the distribution**, and (b) **draw a box-and-whisker plot** using the following data set:
\[6, 23, 17, 23, 35, 45, 17, 44, 25, 35, 39, 49, 45, 56\]
Here's the data set for reference:
\[6, 23, 17, 23, 35, 45, 17, 44, 25, 35, 39, 49, 45, 56\]
...
#### Solution
(a) **Calculate the Five-Number Summary** for this data set:
When calculating the five-number summary, we follow these steps: Identify the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
- **Arrange the data in ascending order:**
\[6, 17, 17, 23, 23, 25, 35, 35, 39, 44, 45, 45, 49, 56\]
- **Minimum:** The smallest number in the data set.
\[\text{Minimum} = 6\]
- **First Quartile (Q1):** The median of the first half of the data set.
\[Q1 = \frac{17 + 23}{2} = 20\] *since 17 and 23 are the 4th and 5th values*
- **Median (Q2):** The middle value of the data set.
\[Q2 = \frac{35 + 35}{2} = 35\] *since 35 and 35 are the 7th and 8th values*
- **Third Quartile (Q3):** The median of the second half of the data set.
\[Q3 = \frac{44 + 45}{2} = 44.5\] *since 44 and 45 are the 10th and 11th values*
- **Maximum:** The largest number in the data set.
\[\text{Maximum} = 56\]
Thus, the five-number summary is:
\[6, 20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F128593f5-7ea4-4e3b-94cd-55abf91c7165%2Fe7099c48-dcac-4167-8fd5-c9aebcd438cf%2F6m4t4qk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Resource on Five-Number Summary and Box-and-Whisker Plot
#### Problem Statement
(a) **Give the five-number summary for the distribution**, and (b) **draw a box-and-whisker plot** using the following data set:
\[6, 23, 17, 23, 35, 45, 17, 44, 25, 35, 39, 49, 45, 56\]
Here's the data set for reference:
\[6, 23, 17, 23, 35, 45, 17, 44, 25, 35, 39, 49, 45, 56\]
...
#### Solution
(a) **Calculate the Five-Number Summary** for this data set:
When calculating the five-number summary, we follow these steps: Identify the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
- **Arrange the data in ascending order:**
\[6, 17, 17, 23, 23, 25, 35, 35, 39, 44, 45, 45, 49, 56\]
- **Minimum:** The smallest number in the data set.
\[\text{Minimum} = 6\]
- **First Quartile (Q1):** The median of the first half of the data set.
\[Q1 = \frac{17 + 23}{2} = 20\] *since 17 and 23 are the 4th and 5th values*
- **Median (Q2):** The middle value of the data set.
\[Q2 = \frac{35 + 35}{2} = 35\] *since 35 and 35 are the 7th and 8th values*
- **Third Quartile (Q3):** The median of the second half of the data set.
\[Q3 = \frac{44 + 45}{2} = 44.5\] *since 44 and 45 are the 10th and 11th values*
- **Maximum:** The largest number in the data set.
\[\text{Maximum} = 56\]
Thus, the five-number summary is:
\[6, 20
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