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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### 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
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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