(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 37 8 4 2 9 8 6 9 4 9 3 2 4 2 98 669 (a) Min = (Simplify your answer.)
(a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 37 8 4 2 9 8 6 9 4 9 3 2 4 2 98 669 (a) Min = (Simplify your answer.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Instructions for Finding the Five-Number Summary and Drawing a Box-and-Whisker Plot
**Problem Statement:**
1. **Task (a):** Find the five-number summary of the given data set.
2. **Task (b):** Draw a box-and-whisker plot of the data.
#### Data Set:
\[ 3, 7, 8, 4, 2, 9, 8, 6, 9, 4, 9, 3, 2, 4, 2, 9, 8, 6, 6, 9 \]
#### Step-by-Step Solution for Task (a):
**Finding the Five-Number Summary**
1. **Min:** (Simplify your answer.)
The five-number summary consists of the following values:
- **Minimum (Min):** The smallest value in the data set.
- **First Quartile (Q1):** The median of the lower half of the data (excluding the median if the number of observations is odd).
- **Median (Q2):** The middle value of the data set.
- **Third Quartile (Q3):** The median of the upper half of the data (excluding the median if the number of observations is odd).
- **Maximum (Max):** The largest value in the data set.
To find the above values, follow these steps:
1. **Sort the Data:** Arrange the data in ascending order.
2. **Identify the Minimum and Maximum:** The first and last values in the sorted list.
3. **Calculate the Median (Q2):** The middle value(s) of the sorted data.
4. **Determine the Quartiles (Q1 and Q3):** The medians of the lower and upper halves of the sorted data.
By following these steps, you can accurately find the five-number summary and subsequently use it to draw a box-and-whisker plot in step (b).
**Note:** Since the specific values for the five-number summary have not been calculated here, you will need to sort the data and perform these calculations on your own.
---
This instruction aims to help students understand the process of finding the five-number summary and encourages them to practice by solving the problem independently.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cb3c841-0ebf-45b6-94fa-bf7d2c1f5291%2F1de78739-3009-4a26-8719-70c4df395640%2Fr5kh63f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Instructions for Finding the Five-Number Summary and Drawing a Box-and-Whisker Plot
**Problem Statement:**
1. **Task (a):** Find the five-number summary of the given data set.
2. **Task (b):** Draw a box-and-whisker plot of the data.
#### Data Set:
\[ 3, 7, 8, 4, 2, 9, 8, 6, 9, 4, 9, 3, 2, 4, 2, 9, 8, 6, 6, 9 \]
#### Step-by-Step Solution for Task (a):
**Finding the Five-Number Summary**
1. **Min:** (Simplify your answer.)
The five-number summary consists of the following values:
- **Minimum (Min):** The smallest value in the data set.
- **First Quartile (Q1):** The median of the lower half of the data (excluding the median if the number of observations is odd).
- **Median (Q2):** The middle value of the data set.
- **Third Quartile (Q3):** The median of the upper half of the data (excluding the median if the number of observations is odd).
- **Maximum (Max):** The largest value in the data set.
To find the above values, follow these steps:
1. **Sort the Data:** Arrange the data in ascending order.
2. **Identify the Minimum and Maximum:** The first and last values in the sorted list.
3. **Calculate the Median (Q2):** The middle value(s) of the sorted data.
4. **Determine the Quartiles (Q1 and Q3):** The medians of the lower and upper halves of the sorted data.
By following these steps, you can accurately find the five-number summary and subsequently use it to draw a box-and-whisker plot in step (b).
**Note:** Since the specific values for the five-number summary have not been calculated here, you will need to sort the data and perform these calculations on your own.
---
This instruction aims to help students understand the process of finding the five-number summary and encourages them to practice by solving the problem independently.
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