### Understanding the 5-Number Summary and Box Plot**Problem Statement:**Calculate the 5-number summary of this numerical distribution, and also the Interquartile Range (IQR) and outlier boundaries. Draw a box plot to show all that information.#### Given Data:18, 14, 27, 35, 7, 16, 21, 20, 28, 19**Steps to Solve:**#### 1. Arrange the Data in Ascending Order:7, 14, 16, 18, 19, 20, 21, 27, 28, 35#### 2. Calculate the 5-Number Summary:- **Minimum (Min):** The smallest number in the data set. - Min = 7- **First Quartile (Q1):** The median of the first half of the data. - Q1 = 16- **Median (Q2):** The middle number of the data set. - Q2 = 19.5 (average of 19 and 20)- **Third Quartile (Q3):** The median of the second half of the data. - Q3 = 27- **Maximum (Max):** The largest number in the data set. - Max = 35- **5-Number Summary:** 7, 16, 19.5, 27, 35#### 3. Calculate the Interquartile Range (IQR):- **IQR = Q3 - Q1** - IQR = 27 - 16 = 11#### 4. Determine the Outlier Boundaries:- **Lower Bound:** - $ Q1 - 1.5 \times IQR $ - Lower Bound = $ 16 - 1.5 \times 11 = 16 - 16.5 = -0.5 $- **Upper Bound:** - $ Q3 + 1.5 \times IQR $ - Upper Bound = $ 27 + 1.5 \times 11 = 27 + 16.5 = 43.5 $#### 5. Draw the Box Plot:- **Box Plot Elements:** - **Whiskers:** Extend from Min to Q1 and from Q3 to Max. -

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Math

Statistics

undaries. Draw a box plot to show all that information. 18, 14, 27, 35, 7, 16, 21, 20, 28, 19

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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Concept explainers

Bar Graphs

A bar graph is a chart or graphical representation of data. A bar chart, also known as a bar graph, is a graph or chart that displays categorical data using rectangular bars with heights or lengths equal to the values they represent. Typically, bar graphs show categorical and numerical variables grouped in class intervals. A bar graph is useful for comparing and analyzing a set of data.

Question

### Understanding the 5-Number Summary and Box Plot

**Problem Statement:**
Calculate the 5-number summary of this numerical distribution, and also the Interquartile Range (IQR) and outlier boundaries. Draw a box plot to show all that information.

#### Given Data:
18, 14, 27, 35, 7, 16, 21, 20, 28, 19

**Steps to Solve:**

#### 1. Arrange the Data in Ascending Order:
7, 14, 16, 18, 19, 20, 21, 27, 28, 35

#### 2. Calculate the 5-Number Summary:
- **Minimum (Min):** The smallest number in the data set.
- Min = 7
- **First Quartile (Q1):** The median of the first half of the data.
- Q1 = 16
- **Median (Q2):** The middle number of the data set.
- Q2 = 19.5 (average of 19 and 20)
- **Third Quartile (Q3):** The median of the second half of the data.
- Q3 = 27
- **Maximum (Max):** The largest number in the data set.
- Max = 35

- **5-Number Summary:** 7, 16, 19.5, 27, 35

#### 3. Calculate the Interquartile Range (IQR):
- **IQR = Q3 - Q1**
- IQR = 27 - 16 = 11

#### 4. Determine the Outlier Boundaries:
- **Lower Bound:**
- $ Q1 - 1.5 \times IQR $
- Lower Bound = $ 16 - 1.5 \times 11 = 16 - 16.5 = -0.5 $
- **Upper Bound:**
- $ Q3 + 1.5 \times IQR $
- Upper Bound = $ 27 + 1.5 \times 11 = 27 + 16.5 = 43.5 $

#### 5. Draw the Box Plot:
- **Box Plot Elements:**
- **Whiskers:** Extend from Min to Q1 and from Q3 to Max.
-

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